Stochastic processes :: fundamentals and emerging applications /
"This book contains 12 chapters describing recent advancements in the theory and applications of stochastic processes. It contains a review of studies of the asymptotic behavior of extremal values of random variables and stochastic processes, description of properties of stochastic models of po...
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Nova Science Publishers,
[2023]
|
| Schriftenreihe: | Mathematics research developments
|
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | "This book contains 12 chapters describing recent advancements in the theory and applications of stochastic processes. It contains a review of studies of the asymptotic behavior of extremal values of random variables and stochastic processes, description of properties of stochastic models of population dynamics under the influence of environmental noise, reviews of methods of modeling of stochastic processes according to its probabilistic and statistical properties in various spaces of random variables with given reliability and accuracy, solution of the problem of mean square optimal estimation of unobserved values of periodically correlated stochastic sequences, and investigation of stability of time-inhomogeneous Markov chains"-- |
| Beschreibung: | 1 online resource. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9798886974751 |
Internformat
MARC
| LEADER | 00000cam a22000008i 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-on1362513194 | ||
| 003 | OCoLC | ||
| 005 | 20250103110447.0 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 221201s2023 nyu ob 001 0 eng | ||
| 010 | |a 2022057364 | ||
| 040 | |a DLC |b eng |e rda |c DLC |d UKAHL |d OCLCF |d N$T |d OCLCO |d QGK |d UKKRT | ||
| 020 | |a 9798886974751 |q (electronic bk.) | ||
| 020 | |z 9781685079826 |q (hardcover) | ||
| 035 | |a (OCoLC)1362513194 | ||
| 042 | |a pcc | ||
| 050 | 0 | 0 | |a QA274 |
| 082 | 7 | |a 519.2/3 |2 23/eng20230117 | |
| 049 | |a MAIN | ||
| 245 | 0 | 0 | |a Stochastic processes : |b fundamentals and emerging applications / |c Mikhail Moklyachuk, D.Sci. (editor), Professor, Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. |
| 263 | |a 2301 | ||
| 264 | 1 | |a New York : |b Nova Science Publishers, |c [2023] | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics research developments | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a "This book contains 12 chapters describing recent advancements in the theory and applications of stochastic processes. It contains a review of studies of the asymptotic behavior of extremal values of random variables and stochastic processes, description of properties of stochastic models of population dynamics under the influence of environmental noise, reviews of methods of modeling of stochastic processes according to its probabilistic and statistical properties in various spaces of random variables with given reliability and accuracy, solution of the problem of mean square optimal estimation of unobserved values of periodically correlated stochastic sequences, and investigation of stability of time-inhomogeneous Markov chains"-- |c Provided by publisher. | ||
| 588 | |a Description based on print version record and CIP data provided by publisher; resource not viewed. | ||
| 505 | 0 | |a Intro -- Stochastic ProcessesFundamentals and Emerging Applications -- Contents -- Preface -- Chapter 1Asymptotic Behavior of Extreme Values of RandomVariables and Some Stochastic Processes -- Abstract -- 1. Introduction -- 2. Asymptotic Behavior of Extreme Values ofRandom Variables -- 2.1. Some Early Results -- 2.2. Law of the Iterated Logarithm and a Law of the Triple Logarithm andIts Generalization -- 2.3. "Confidence Intervals" for Extrema of Discrete Random Variables -- 3. Asymptotic Behavior of Extreme Valuesof Regenerative Processes -- 3.1. General Regenerative Processes -- 3.2. Birth and Death Processes -- 3.3. Processes in Queuing Systems -- Conclusion -- References -- Chapter 2Long-Time Behavior of Stochastic Models ofPopulation Dynamics with Jumps -- Abstract -- 1. Introduction -- 2. Stochastic Non-Autonomous Logistic Modelswith Jumps -- 2.1. Definitions and Notations -- 2.2. Non-Autonomous Stochastic Logistic Differential Equation with LinearRandom Perturbations -- 2.3. Logistic Model with Periodical Coefficients -- 2.4. Related Stochastic Differential Equation -- 2.5. Non-Autonomous Stochastic Logistic Differential Equation withNon-Linear Random Perturbations -- 3. Stochastic Two-SpeciesMutualism Model with Jumps -- 3.1. Notations and Definitions -- 3.2. Long-Time Behavior of StochasticMutualismModel -- 4. A Non-Autonomous Stochastic Predator-PreyModelswith Jumps -- 4.1. A Non-Autonomous Predator-Prey Model with a Modified Versionof Leslie-Gower Term and Holling-Type II Functional Response -- 4.2. A Predator-Prey Model with Beddington-DeAngelis FunctionalResponse -- Conclusion -- References -- Chapter 3Modeling and Simulation of Stochastic Processes -- Abstract -- Introduction -- Generation of a Gaussian Process -- Method of Linear Filters -- Gaussian White Noise -- Linear Filters -- Series Expansion with Random Amplitudes. | |
| 505 | 8 | |a Series Expansion with Random Phases -- Series Expansion with Random Amplitudes and Random Phases -- Generation of a Non-Gaussian Process -- Method of Nonlinear Filters -- Low-Pass Processes -- Processes Defined in Infinite Interval -- Processes Defined in Semi-Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Spectrum Peaks at Non-Zero Frequencies -- Processes Defined in Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Multiple Spectrum Peaks -- Randomized Harmonic Model -- Randomized Harmonic Processes with One Spectrum Peak -- Randomized Harmonic Processes with Multiple Spectrum Peaks -- Monte Carlo Simulation of Randomized Harmonic Processes -- Generation of Two Correlated Gaussian Processes -- Method of Linear Filters -- Two Correlated Gaussian Random Variables -- Two Correlated Gaussian White Noises -- Two Correlated Gaussian Processes -- Series Expansion with Random Amplitudes -- Series Expansion with Random Phases -- Conclusion -- References -- Chapter 4Estimation Problems for Periodically CorrelatedStochastic Sequences with Missed Observations -- Abstract -- 1. Introduction -- 2. Periodically Correlated Sequences and MultidimensionalStationary Sequences -- 3. The Hilbert Space ProjectionMethod of Extrapolationof Functionals -- 3.1. Extrapolation of Functionals from Observations without Noise -- 3.2. Extrapolation of Finite Sum Functionals -- 4. Minimax (Robust) Method of Linear Extrapolation -- 4.1. The Least Favorable Spectral Densities in the Class D = D0 × DU -- 4.2. The Least Favorable Spectral Densities in the Class D = D" × D -- 5. The Hilbert Space ProjectionMethod of Interpolationof Functionals -- 5.1. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 1 -- 5.2. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 2. | |
| 505 | 8 | |a 6. Minimax (Robust) Method of Linear Interpolation -- 6.1. The Least Favorable Spectral Densities in D− -- 6.2. The Least Favorable Spectral Densities in D− -- Conclusion -- References -- Chapter 5Coupling Method in Studying Stabilityof Time-InhomogeneousMarkov Chains -- Abstract -- 1. Introduction -- 2. Coupling of Two Chains -- 3. UniformMinorization Case -- 4. Relaxing the Proximity Condition -- 5. Nonuniform Minorization -- 6. Renewal Process Generated by a Pair of InhomogeneousMarkov Chains -- 6.1. Dependence of Renewal Moments for Time-InhomogeneousMarkov Chain -- 6.2. Key Definitions -- 6.3. Formal Definition of the l(t) Variable -- Conclusion -- References -- Chapter 6Minimax Prediction of Sequences with PeriodicallyStationary Increments Observed with Noise andCointegrated Sequences -- Abstract -- 1. Introduction -- 2. Stochastic Sequences with Periodically StationaryIncrements -- 3. Hilbert Space ProjectionMethod of Prediction -- 3.1. Prediction of Vector-Valued Stochastic Sequences withStationary Increments -- 3.2. Prediction Based on Factorizations of the Spectral Densities -- 3.3. Prediction of Stochastic Sequences with Periodically StationaryIncrement -- 3.4. Prediction of One Class of Cointegrated Vector Stochastic Sequences -- 4. Minimax (Robust) Method of Prediction -- 4.1. Least Favorable Spectral Density in Classes D0 × D1 -- 4.2. Least Favorable Spectral Density in Classes D0 × D1 for CointegratedVector Sequences -- 4.3. Least Favorable Spectral Density in Classes D" × DU -- 4.4. Least Favorable Spectral Density for Cointegrated Vector Sequences inClasses D" × DU -- Conclusion -- References -- Chapter 7Estimation of Multidimensional Stationary StochasticSequences from Observations in Special Sets of Points -- Abstract -- 1. Introduction -- 2. The Hilbert Space ProjectionMethod of LinearEstimation. | |
| 505 | 8 | |a 3. Minimax-RobustMethod of Interpolation -- 4. Least Favourable Spectral Densities in the Class D0,0 -- 5. Least Favourable Spectral Densities in Classes DUV × D -- 6. Least Favourable Spectral Densities in Classes D1"1 × D2"2 -- 7. Least Favourable Spectral Densities in the Class D− -- 8. Least Favourable Spectral Densities in the Class DW -- 9. Least Favourable Spectral Densities in the Class DU -- Conclusion -- References -- Chapter 8Invariant Measures and Asymptotic Behavior ofStochastic Evolution Equations -- Abstract -- 1. Introduction -- 2. Bounded Solutions and InvariantMeasures inWeighted Spaces -- 2.1. Strong Dissipation: Exponentially Contractive Semigroup -- 2.2. Weak Dissipation -- 2.2.1. Proof of Theorem 8. Preliminary Facts -- 2.2.2. Ito's Formula -- 2.2.3. The Relation between Ito's Formula and Weak Solutions -- 3. Asymptotic Results for Invariant Measures -- 3.1. Vanishing Dissipation Limit -- 3.2. Homogenization -- 3.2.1. Homogenization Notation and Preliminaries -- 3.2.2. Nash-Aranson Estimates. Semigroup Estimates -- 3.2.3. Proof of Theorem 14 -- 4. Existence of InvariantMeasure for SPDEs withNon-Lipschitz Coefficients -- 4.1. Existence of InvariantMeasure -- 4.2. Uniquences of InvariantMeasure -- 4.3. Examples. -- 4.3.1. Local Elliptic Operator -- 4.3.2. Nonlocal Elliptic Operator -- 4.3.3. Allen-Cahn Nonlinearity -- Conclusion -- Acknowledgments -- References -- Chapter 9Quasi-Banach Spaces of Random Variables andModeling of Stochastic Processes -- Abstract -- 1. Introduction -- 2. Pre-Banach Spaces DV,W of Random Variables -- 2.1. Basic Definitions -- 2.2. Spaces DV,W() of Random Variables -- 2.3. Convergence of Series in the Spaces DV,W(). -- 2.4. Convergence of Infinite Sums of Random Variables withSpecific Distributionsin the Space DV,W -- 2.5. Stochastic Processes in the Space DV,W. | |
| 505 | 8 | |a 2.6. Boundedness of the Supremumof Stochastic Processes in the SpaceDV,W -- 2.7. Continuity of stochastic processes belonging to the spaces DV,W -- 2.8. Uniform Convergence of Function Series in DV,W -- 2.9. Models of Stochastic Processes from the Space DV,W -- 2.10. Examples of Models of Stochastic Processes from the Space DV,W() -- 3. Modeling of Stochastic Processes in Lp(T) UsingApproximated Decompositions -- 3.1. Basic Definitions -- 3.2. Modeling of Stochastic Processes in Lp(T ) Using OrthogonalPolynomials -- 3.3. Modeling of Stochastic Processes in Lp(0, T ) Using the HermitePolynomials -- 3.4. Modeling of Stochastic Processes in Lp(0, T ) Using the ChebyshevPolynomials -- 4. Models of '-Sub-Gaussian Stochastic Processes in C(T)Spaces -- 4.1. Models of Stochastic Processes in C(T ) That Allow Representation inSeries with Independent Elements -- Conclusion -- References -- Chapter 10Simulation of Stochastic Processes with GivenReliability and Accuracy -- Abstract -- 1. Introduction -- 2. Simulation of Stationary Random Sequences -- 2.1. Basic Definitions -- 2.2. Spectral Decomposition of Stationary Random Sequence -- 2.3. '-Sub-Gaussian Random Variables -- 2.4. Main Results of the Section 2 -- 2.5. The Case Study -- 2.5.1. The AR(1) Sequence -- 2.5.2. The ARMA(1,1) Sequence -- 3. Methods of StatisticalModeling of StochasticProcesses Represented in the Form of Series -- 3.1. Convergence of Strictly Sub-Gaussian Random Series in L2(T ) -- 3.2. Accuracy and Reliability of StatisticalModeling of Sub-GaussianHomogeneous Random Fields on a Sphere -- 4. Simulation of Stochastic Processes as Input on a System Tak-ing into Account the System Response -- 4.1. Space of Square-Gaussian Random Variables and Square-GaussianStochastic Processes -- 4.2. The Distribution of Supremums of Square-Gaussian StochasticProcesses. | |
| 650 | 0 | |a Stochastic processes. |0 http://id.loc.gov/authorities/subjects/sh85128181 | |
| 650 | 0 | |a Stochastic processes |x Mathematical models. | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 6 | |a Processus stochastiques |x Modèles mathématiques. | |
| 650 | 7 | |a Stochastic processes |2 fast | |
| 650 | 7 | |a Stochastic processes |x Mathematical models |2 fast | |
| 700 | 1 | |a Moklyachuk, Mikhail P., |e editor. | |
| 776 | 0 | 8 | |i Print version: |t Stochastic processes |d New York : Nova Science Publishers, [2023] |z 9781685079826 |w (DLC) 2022057363 |
| 966 | 4 | 0 | |l DE-862 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=3456150 |3 Volltext |
| 966 | 4 | 0 | |l DE-863 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=3456150 |3 Volltext |
| 938 | |a Kortext |b KTXT |n 2144837 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH41091122 | ||
| 938 | |a EBSCOhost |b EBSC |n 3456150 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-862 | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-on1362513194 |
|---|---|
| _version_ | 1829095378157305856 |
| adam_text | |
| any_adam_object | |
| author2 | Moklyachuk, Mikhail P. |
| author2_role | edt |
| author2_variant | m p m mp mpm |
| author_facet | Moklyachuk, Mikhail P. |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274 |
| callnumber-search | QA274 |
| callnumber-sort | QA 3274 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Intro -- Stochastic ProcessesFundamentals and Emerging Applications -- Contents -- Preface -- Chapter 1Asymptotic Behavior of Extreme Values of RandomVariables and Some Stochastic Processes -- Abstract -- 1. Introduction -- 2. Asymptotic Behavior of Extreme Values ofRandom Variables -- 2.1. Some Early Results -- 2.2. Law of the Iterated Logarithm and a Law of the Triple Logarithm andIts Generalization -- 2.3. "Confidence Intervals" for Extrema of Discrete Random Variables -- 3. Asymptotic Behavior of Extreme Valuesof Regenerative Processes -- 3.1. General Regenerative Processes -- 3.2. Birth and Death Processes -- 3.3. Processes in Queuing Systems -- Conclusion -- References -- Chapter 2Long-Time Behavior of Stochastic Models ofPopulation Dynamics with Jumps -- Abstract -- 1. Introduction -- 2. Stochastic Non-Autonomous Logistic Modelswith Jumps -- 2.1. Definitions and Notations -- 2.2. Non-Autonomous Stochastic Logistic Differential Equation with LinearRandom Perturbations -- 2.3. Logistic Model with Periodical Coefficients -- 2.4. Related Stochastic Differential Equation -- 2.5. Non-Autonomous Stochastic Logistic Differential Equation withNon-Linear Random Perturbations -- 3. Stochastic Two-SpeciesMutualism Model with Jumps -- 3.1. Notations and Definitions -- 3.2. Long-Time Behavior of StochasticMutualismModel -- 4. A Non-Autonomous Stochastic Predator-PreyModelswith Jumps -- 4.1. A Non-Autonomous Predator-Prey Model with a Modified Versionof Leslie-Gower Term and Holling-Type II Functional Response -- 4.2. A Predator-Prey Model with Beddington-DeAngelis FunctionalResponse -- Conclusion -- References -- Chapter 3Modeling and Simulation of Stochastic Processes -- Abstract -- Introduction -- Generation of a Gaussian Process -- Method of Linear Filters -- Gaussian White Noise -- Linear Filters -- Series Expansion with Random Amplitudes. Series Expansion with Random Phases -- Series Expansion with Random Amplitudes and Random Phases -- Generation of a Non-Gaussian Process -- Method of Nonlinear Filters -- Low-Pass Processes -- Processes Defined in Infinite Interval -- Processes Defined in Semi-Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Spectrum Peaks at Non-Zero Frequencies -- Processes Defined in Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Multiple Spectrum Peaks -- Randomized Harmonic Model -- Randomized Harmonic Processes with One Spectrum Peak -- Randomized Harmonic Processes with Multiple Spectrum Peaks -- Monte Carlo Simulation of Randomized Harmonic Processes -- Generation of Two Correlated Gaussian Processes -- Method of Linear Filters -- Two Correlated Gaussian Random Variables -- Two Correlated Gaussian White Noises -- Two Correlated Gaussian Processes -- Series Expansion with Random Amplitudes -- Series Expansion with Random Phases -- Conclusion -- References -- Chapter 4Estimation Problems for Periodically CorrelatedStochastic Sequences with Missed Observations -- Abstract -- 1. Introduction -- 2. Periodically Correlated Sequences and MultidimensionalStationary Sequences -- 3. The Hilbert Space ProjectionMethod of Extrapolationof Functionals -- 3.1. Extrapolation of Functionals from Observations without Noise -- 3.2. Extrapolation of Finite Sum Functionals -- 4. Minimax (Robust) Method of Linear Extrapolation -- 4.1. The Least Favorable Spectral Densities in the Class D = D0 × DU -- 4.2. The Least Favorable Spectral Densities in the Class D = D" × D -- 5. The Hilbert Space ProjectionMethod of Interpolationof Functionals -- 5.1. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 1 -- 5.2. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 2. 6. Minimax (Robust) Method of Linear Interpolation -- 6.1. The Least Favorable Spectral Densities in D− -- 6.2. The Least Favorable Spectral Densities in D− -- Conclusion -- References -- Chapter 5Coupling Method in Studying Stabilityof Time-InhomogeneousMarkov Chains -- Abstract -- 1. Introduction -- 2. Coupling of Two Chains -- 3. UniformMinorization Case -- 4. Relaxing the Proximity Condition -- 5. Nonuniform Minorization -- 6. Renewal Process Generated by a Pair of InhomogeneousMarkov Chains -- 6.1. Dependence of Renewal Moments for Time-InhomogeneousMarkov Chain -- 6.2. Key Definitions -- 6.3. Formal Definition of the l(t) Variable -- Conclusion -- References -- Chapter 6Minimax Prediction of Sequences with PeriodicallyStationary Increments Observed with Noise andCointegrated Sequences -- Abstract -- 1. Introduction -- 2. Stochastic Sequences with Periodically StationaryIncrements -- 3. Hilbert Space ProjectionMethod of Prediction -- 3.1. Prediction of Vector-Valued Stochastic Sequences withStationary Increments -- 3.2. Prediction Based on Factorizations of the Spectral Densities -- 3.3. Prediction of Stochastic Sequences with Periodically StationaryIncrement -- 3.4. Prediction of One Class of Cointegrated Vector Stochastic Sequences -- 4. Minimax (Robust) Method of Prediction -- 4.1. Least Favorable Spectral Density in Classes D0 × D1 -- 4.2. Least Favorable Spectral Density in Classes D0 × D1 for CointegratedVector Sequences -- 4.3. Least Favorable Spectral Density in Classes D" × DU -- 4.4. Least Favorable Spectral Density for Cointegrated Vector Sequences inClasses D" × DU -- Conclusion -- References -- Chapter 7Estimation of Multidimensional Stationary StochasticSequences from Observations in Special Sets of Points -- Abstract -- 1. Introduction -- 2. The Hilbert Space ProjectionMethod of LinearEstimation. 3. Minimax-RobustMethod of Interpolation -- 4. Least Favourable Spectral Densities in the Class D0,0 -- 5. Least Favourable Spectral Densities in Classes DUV × D -- 6. Least Favourable Spectral Densities in Classes D1"1 × D2"2 -- 7. Least Favourable Spectral Densities in the Class D− -- 8. Least Favourable Spectral Densities in the Class DW -- 9. Least Favourable Spectral Densities in the Class DU -- Conclusion -- References -- Chapter 8Invariant Measures and Asymptotic Behavior ofStochastic Evolution Equations -- Abstract -- 1. Introduction -- 2. Bounded Solutions and InvariantMeasures inWeighted Spaces -- 2.1. Strong Dissipation: Exponentially Contractive Semigroup -- 2.2. Weak Dissipation -- 2.2.1. Proof of Theorem 8. Preliminary Facts -- 2.2.2. Ito's Formula -- 2.2.3. The Relation between Ito's Formula and Weak Solutions -- 3. Asymptotic Results for Invariant Measures -- 3.1. Vanishing Dissipation Limit -- 3.2. Homogenization -- 3.2.1. Homogenization Notation and Preliminaries -- 3.2.2. Nash-Aranson Estimates. Semigroup Estimates -- 3.2.3. Proof of Theorem 14 -- 4. Existence of InvariantMeasure for SPDEs withNon-Lipschitz Coefficients -- 4.1. Existence of InvariantMeasure -- 4.2. Uniquences of InvariantMeasure -- 4.3. Examples. -- 4.3.1. Local Elliptic Operator -- 4.3.2. Nonlocal Elliptic Operator -- 4.3.3. Allen-Cahn Nonlinearity -- Conclusion -- Acknowledgments -- References -- Chapter 9Quasi-Banach Spaces of Random Variables andModeling of Stochastic Processes -- Abstract -- 1. Introduction -- 2. Pre-Banach Spaces DV,W of Random Variables -- 2.1. Basic Definitions -- 2.2. Spaces DV,W() of Random Variables -- 2.3. Convergence of Series in the Spaces DV,W(). -- 2.4. Convergence of Infinite Sums of Random Variables withSpecific Distributionsin the Space DV,W -- 2.5. Stochastic Processes in the Space DV,W. 2.6. Boundedness of the Supremumof Stochastic Processes in the SpaceDV,W -- 2.7. Continuity of stochastic processes belonging to the spaces DV,W -- 2.8. Uniform Convergence of Function Series in DV,W -- 2.9. Models of Stochastic Processes from the Space DV,W -- 2.10. Examples of Models of Stochastic Processes from the Space DV,W() -- 3. Modeling of Stochastic Processes in Lp(T) UsingApproximated Decompositions -- 3.1. Basic Definitions -- 3.2. Modeling of Stochastic Processes in Lp(T ) Using OrthogonalPolynomials -- 3.3. Modeling of Stochastic Processes in Lp(0, T ) Using the HermitePolynomials -- 3.4. Modeling of Stochastic Processes in Lp(0, T ) Using the ChebyshevPolynomials -- 4. Models of '-Sub-Gaussian Stochastic Processes in C(T)Spaces -- 4.1. Models of Stochastic Processes in C(T ) That Allow Representation inSeries with Independent Elements -- Conclusion -- References -- Chapter 10Simulation of Stochastic Processes with GivenReliability and Accuracy -- Abstract -- 1. Introduction -- 2. Simulation of Stationary Random Sequences -- 2.1. Basic Definitions -- 2.2. Spectral Decomposition of Stationary Random Sequence -- 2.3. '-Sub-Gaussian Random Variables -- 2.4. Main Results of the Section 2 -- 2.5. The Case Study -- 2.5.1. The AR(1) Sequence -- 2.5.2. The ARMA(1,1) Sequence -- 3. Methods of StatisticalModeling of StochasticProcesses Represented in the Form of Series -- 3.1. Convergence of Strictly Sub-Gaussian Random Series in L2(T ) -- 3.2. Accuracy and Reliability of StatisticalModeling of Sub-GaussianHomogeneous Random Fields on a Sphere -- 4. Simulation of Stochastic Processes as Input on a System Tak-ing into Account the System Response -- 4.1. Space of Square-Gaussian Random Variables and Square-GaussianStochastic Processes -- 4.2. The Distribution of Supremums of Square-Gaussian StochasticProcesses. |
| ctrlnum | (OCoLC)1362513194 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
| dewey-sort | 3519.2 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>12244cam a22005538i 4500</leader><controlfield tag="001">ZDB-4-EBA-on1362513194</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20250103110447.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |||||||||||</controlfield><controlfield tag="008">221201s2023 nyu ob 001 0 eng </controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a"> 2022057364</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DLC</subfield><subfield code="b">eng</subfield><subfield code="e">rda</subfield><subfield code="c">DLC</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCF</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCO</subfield><subfield code="d">QGK</subfield><subfield code="d">UKKRT</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9798886974751</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781685079826</subfield><subfield code="q">(hardcover)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1362513194</subfield></datafield><datafield tag="042" ind1=" " ind2=" "><subfield code="a">pcc</subfield></datafield><datafield tag="050" ind1="0" ind2="0"><subfield code="a">QA274</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">519.2/3</subfield><subfield code="2">23/eng20230117</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="245" ind1="0" ind2="0"><subfield code="a">Stochastic processes :</subfield><subfield code="b">fundamentals and emerging applications /</subfield><subfield code="c">Mikhail Moklyachuk, D.Sci. (editor), Professor, Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine.</subfield></datafield><datafield tag="263" ind1=" " ind2=" "><subfield code="a">2301</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York :</subfield><subfield code="b">Nova Science Publishers,</subfield><subfield code="c">[2023]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics research developments</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"This book contains 12 chapters describing recent advancements in the theory and applications of stochastic processes. It contains a review of studies of the asymptotic behavior of extremal values of random variables and stochastic processes, description of properties of stochastic models of population dynamics under the influence of environmental noise, reviews of methods of modeling of stochastic processes according to its probabilistic and statistical properties in various spaces of random variables with given reliability and accuracy, solution of the problem of mean square optimal estimation of unobserved values of periodically correlated stochastic sequences, and investigation of stability of time-inhomogeneous Markov chains"--</subfield><subfield code="c">Provided by publisher.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on print version record and CIP data provided by publisher; resource not viewed.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Intro -- Stochastic ProcessesFundamentals and Emerging Applications -- Contents -- Preface -- Chapter 1Asymptotic Behavior of Extreme Values of RandomVariables and Some Stochastic Processes -- Abstract -- 1. Introduction -- 2. Asymptotic Behavior of Extreme Values ofRandom Variables -- 2.1. Some Early Results -- 2.2. Law of the Iterated Logarithm and a Law of the Triple Logarithm andIts Generalization -- 2.3. "Confidence Intervals" for Extrema of Discrete Random Variables -- 3. Asymptotic Behavior of Extreme Valuesof Regenerative Processes -- 3.1. General Regenerative Processes -- 3.2. Birth and Death Processes -- 3.3. Processes in Queuing Systems -- Conclusion -- References -- Chapter 2Long-Time Behavior of Stochastic Models ofPopulation Dynamics with Jumps -- Abstract -- 1. Introduction -- 2. Stochastic Non-Autonomous Logistic Modelswith Jumps -- 2.1. Definitions and Notations -- 2.2. Non-Autonomous Stochastic Logistic Differential Equation with LinearRandom Perturbations -- 2.3. Logistic Model with Periodical Coefficients -- 2.4. Related Stochastic Differential Equation -- 2.5. Non-Autonomous Stochastic Logistic Differential Equation withNon-Linear Random Perturbations -- 3. Stochastic Two-SpeciesMutualism Model with Jumps -- 3.1. Notations and Definitions -- 3.2. Long-Time Behavior of StochasticMutualismModel -- 4. A Non-Autonomous Stochastic Predator-PreyModelswith Jumps -- 4.1. A Non-Autonomous Predator-Prey Model with a Modified Versionof Leslie-Gower Term and Holling-Type II Functional Response -- 4.2. A Predator-Prey Model with Beddington-DeAngelis FunctionalResponse -- Conclusion -- References -- Chapter 3Modeling and Simulation of Stochastic Processes -- Abstract -- Introduction -- Generation of a Gaussian Process -- Method of Linear Filters -- Gaussian White Noise -- Linear Filters -- Series Expansion with Random Amplitudes.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Series Expansion with Random Phases -- Series Expansion with Random Amplitudes and Random Phases -- Generation of a Non-Gaussian Process -- Method of Nonlinear Filters -- Low-Pass Processes -- Processes Defined in Infinite Interval -- Processes Defined in Semi-Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Spectrum Peaks at Non-Zero Frequencies -- Processes Defined in Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Multiple Spectrum Peaks -- Randomized Harmonic Model -- Randomized Harmonic Processes with One Spectrum Peak -- Randomized Harmonic Processes with Multiple Spectrum Peaks -- Monte Carlo Simulation of Randomized Harmonic Processes -- Generation of Two Correlated Gaussian Processes -- Method of Linear Filters -- Two Correlated Gaussian Random Variables -- Two Correlated Gaussian White Noises -- Two Correlated Gaussian Processes -- Series Expansion with Random Amplitudes -- Series Expansion with Random Phases -- Conclusion -- References -- Chapter 4Estimation Problems for Periodically CorrelatedStochastic Sequences with Missed Observations -- Abstract -- 1. Introduction -- 2. Periodically Correlated Sequences and MultidimensionalStationary Sequences -- 3. The Hilbert Space ProjectionMethod of Extrapolationof Functionals -- 3.1. Extrapolation of Functionals from Observations without Noise -- 3.2. Extrapolation of Finite Sum Functionals -- 4. Minimax (Robust) Method of Linear Extrapolation -- 4.1. The Least Favorable Spectral Densities in the Class D = D0 × DU -- 4.2. The Least Favorable Spectral Densities in the Class D = D" × D -- 5. The Hilbert Space ProjectionMethod of Interpolationof Functionals -- 5.1. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 1 -- 5.2. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 2.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6. Minimax (Robust) Method of Linear Interpolation -- 6.1. The Least Favorable Spectral Densities in D− -- 6.2. The Least Favorable Spectral Densities in D− -- Conclusion -- References -- Chapter 5Coupling Method in Studying Stabilityof Time-InhomogeneousMarkov Chains -- Abstract -- 1. Introduction -- 2. Coupling of Two Chains -- 3. UniformMinorization Case -- 4. Relaxing the Proximity Condition -- 5. Nonuniform Minorization -- 6. Renewal Process Generated by a Pair of InhomogeneousMarkov Chains -- 6.1. Dependence of Renewal Moments for Time-InhomogeneousMarkov Chain -- 6.2. Key Definitions -- 6.3. Formal Definition of the l(t) Variable -- Conclusion -- References -- Chapter 6Minimax Prediction of Sequences with PeriodicallyStationary Increments Observed with Noise andCointegrated Sequences -- Abstract -- 1. Introduction -- 2. Stochastic Sequences with Periodically StationaryIncrements -- 3. Hilbert Space ProjectionMethod of Prediction -- 3.1. Prediction of Vector-Valued Stochastic Sequences withStationary Increments -- 3.2. Prediction Based on Factorizations of the Spectral Densities -- 3.3. Prediction of Stochastic Sequences with Periodically StationaryIncrement -- 3.4. Prediction of One Class of Cointegrated Vector Stochastic Sequences -- 4. Minimax (Robust) Method of Prediction -- 4.1. Least Favorable Spectral Density in Classes D0 × D1 -- 4.2. Least Favorable Spectral Density in Classes D0 × D1 for CointegratedVector Sequences -- 4.3. Least Favorable Spectral Density in Classes D" × DU -- 4.4. Least Favorable Spectral Density for Cointegrated Vector Sequences inClasses D" × DU -- Conclusion -- References -- Chapter 7Estimation of Multidimensional Stationary StochasticSequences from Observations in Special Sets of Points -- Abstract -- 1. Introduction -- 2. The Hilbert Space ProjectionMethod of LinearEstimation.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3. Minimax-RobustMethod of Interpolation -- 4. Least Favourable Spectral Densities in the Class D0,0 -- 5. Least Favourable Spectral Densities in Classes DUV × D -- 6. Least Favourable Spectral Densities in Classes D1"1 × D2"2 -- 7. Least Favourable Spectral Densities in the Class D− -- 8. Least Favourable Spectral Densities in the Class DW -- 9. Least Favourable Spectral Densities in the Class DU -- Conclusion -- References -- Chapter 8Invariant Measures and Asymptotic Behavior ofStochastic Evolution Equations -- Abstract -- 1. Introduction -- 2. Bounded Solutions and InvariantMeasures inWeighted Spaces -- 2.1. Strong Dissipation: Exponentially Contractive Semigroup -- 2.2. Weak Dissipation -- 2.2.1. Proof of Theorem 8. Preliminary Facts -- 2.2.2. Ito's Formula -- 2.2.3. The Relation between Ito's Formula and Weak Solutions -- 3. Asymptotic Results for Invariant Measures -- 3.1. Vanishing Dissipation Limit -- 3.2. Homogenization -- 3.2.1. Homogenization Notation and Preliminaries -- 3.2.2. Nash-Aranson Estimates. Semigroup Estimates -- 3.2.3. Proof of Theorem 14 -- 4. Existence of InvariantMeasure for SPDEs withNon-Lipschitz Coefficients -- 4.1. Existence of InvariantMeasure -- 4.2. Uniquences of InvariantMeasure -- 4.3. Examples. -- 4.3.1. Local Elliptic Operator -- 4.3.2. Nonlocal Elliptic Operator -- 4.3.3. Allen-Cahn Nonlinearity -- Conclusion -- Acknowledgments -- References -- Chapter 9Quasi-Banach Spaces of Random Variables andModeling of Stochastic Processes -- Abstract -- 1. Introduction -- 2. Pre-Banach Spaces DV,W of Random Variables -- 2.1. Basic Definitions -- 2.2. Spaces DV,W() of Random Variables -- 2.3. Convergence of Series in the Spaces DV,W(). -- 2.4. Convergence of Infinite Sums of Random Variables withSpecific Distributionsin the Space DV,W -- 2.5. Stochastic Processes in the Space DV,W.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.6. Boundedness of the Supremumof Stochastic Processes in the SpaceDV,W -- 2.7. Continuity of stochastic processes belonging to the spaces DV,W -- 2.8. Uniform Convergence of Function Series in DV,W -- 2.9. Models of Stochastic Processes from the Space DV,W -- 2.10. Examples of Models of Stochastic Processes from the Space DV,W() -- 3. Modeling of Stochastic Processes in Lp(T) UsingApproximated Decompositions -- 3.1. Basic Definitions -- 3.2. Modeling of Stochastic Processes in Lp(T ) Using OrthogonalPolynomials -- 3.3. Modeling of Stochastic Processes in Lp(0, T ) Using the HermitePolynomials -- 3.4. Modeling of Stochastic Processes in Lp(0, T ) Using the ChebyshevPolynomials -- 4. Models of '-Sub-Gaussian Stochastic Processes in C(T)Spaces -- 4.1. Models of Stochastic Processes in C(T ) That Allow Representation inSeries with Independent Elements -- Conclusion -- References -- Chapter 10Simulation of Stochastic Processes with GivenReliability and Accuracy -- Abstract -- 1. Introduction -- 2. Simulation of Stationary Random Sequences -- 2.1. Basic Definitions -- 2.2. Spectral Decomposition of Stationary Random Sequence -- 2.3. '-Sub-Gaussian Random Variables -- 2.4. Main Results of the Section 2 -- 2.5. The Case Study -- 2.5.1. The AR(1) Sequence -- 2.5.2. The ARMA(1,1) Sequence -- 3. Methods of StatisticalModeling of StochasticProcesses Represented in the Form of Series -- 3.1. Convergence of Strictly Sub-Gaussian Random Series in L2(T ) -- 3.2. Accuracy and Reliability of StatisticalModeling of Sub-GaussianHomogeneous Random Fields on a Sphere -- 4. Simulation of Stochastic Processes as Input on a System Tak-ing into Account the System Response -- 4.1. Space of Square-Gaussian Random Variables and Square-GaussianStochastic Processes -- 4.2. The Distribution of Supremums of Square-Gaussian StochasticProcesses.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Stochastic processes.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85128181</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Stochastic processes</subfield><subfield code="x">Mathematical models.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Processus stochastiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Processus stochastiques</subfield><subfield code="x">Modèles mathématiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastic processes</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastic processes</subfield><subfield code="x">Mathematical models</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Moklyachuk, Mikhail P.,</subfield><subfield code="e">editor.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="t">Stochastic processes</subfield><subfield code="d">New York : Nova Science Publishers, [2023]</subfield><subfield code="z">9781685079826</subfield><subfield code="w">(DLC) 2022057363</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-862</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=3456150</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="4" ind2="0"><subfield code="l">DE-863</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=3456150</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Kortext</subfield><subfield code="b">KTXT</subfield><subfield code="n">2144837</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH41091122</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">3456150</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-862</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-on1362513194 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:48:04Z |
| institution | BVB |
| isbn | 9798886974751 |
| language | English |
| lccn | 2022057364 |
| oclc_num | 1362513194 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource. |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | Nova Science Publishers, |
| record_format | marc |
| series2 | Mathematics research developments |
| spelling | Stochastic processes : fundamentals and emerging applications / Mikhail Moklyachuk, D.Sci. (editor), Professor, Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. 2301 New York : Nova Science Publishers, [2023] 1 online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics research developments Includes bibliographical references and index. "This book contains 12 chapters describing recent advancements in the theory and applications of stochastic processes. It contains a review of studies of the asymptotic behavior of extremal values of random variables and stochastic processes, description of properties of stochastic models of population dynamics under the influence of environmental noise, reviews of methods of modeling of stochastic processes according to its probabilistic and statistical properties in various spaces of random variables with given reliability and accuracy, solution of the problem of mean square optimal estimation of unobserved values of periodically correlated stochastic sequences, and investigation of stability of time-inhomogeneous Markov chains"-- Provided by publisher. Description based on print version record and CIP data provided by publisher; resource not viewed. Intro -- Stochastic ProcessesFundamentals and Emerging Applications -- Contents -- Preface -- Chapter 1Asymptotic Behavior of Extreme Values of RandomVariables and Some Stochastic Processes -- Abstract -- 1. Introduction -- 2. Asymptotic Behavior of Extreme Values ofRandom Variables -- 2.1. Some Early Results -- 2.2. Law of the Iterated Logarithm and a Law of the Triple Logarithm andIts Generalization -- 2.3. "Confidence Intervals" for Extrema of Discrete Random Variables -- 3. Asymptotic Behavior of Extreme Valuesof Regenerative Processes -- 3.1. General Regenerative Processes -- 3.2. Birth and Death Processes -- 3.3. Processes in Queuing Systems -- Conclusion -- References -- Chapter 2Long-Time Behavior of Stochastic Models ofPopulation Dynamics with Jumps -- Abstract -- 1. Introduction -- 2. Stochastic Non-Autonomous Logistic Modelswith Jumps -- 2.1. Definitions and Notations -- 2.2. Non-Autonomous Stochastic Logistic Differential Equation with LinearRandom Perturbations -- 2.3. Logistic Model with Periodical Coefficients -- 2.4. Related Stochastic Differential Equation -- 2.5. Non-Autonomous Stochastic Logistic Differential Equation withNon-Linear Random Perturbations -- 3. Stochastic Two-SpeciesMutualism Model with Jumps -- 3.1. Notations and Definitions -- 3.2. Long-Time Behavior of StochasticMutualismModel -- 4. A Non-Autonomous Stochastic Predator-PreyModelswith Jumps -- 4.1. A Non-Autonomous Predator-Prey Model with a Modified Versionof Leslie-Gower Term and Holling-Type II Functional Response -- 4.2. A Predator-Prey Model with Beddington-DeAngelis FunctionalResponse -- Conclusion -- References -- Chapter 3Modeling and Simulation of Stochastic Processes -- Abstract -- Introduction -- Generation of a Gaussian Process -- Method of Linear Filters -- Gaussian White Noise -- Linear Filters -- Series Expansion with Random Amplitudes. Series Expansion with Random Phases -- Series Expansion with Random Amplitudes and Random Phases -- Generation of a Non-Gaussian Process -- Method of Nonlinear Filters -- Low-Pass Processes -- Processes Defined in Infinite Interval -- Processes Defined in Semi-Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Spectrum Peaks at Non-Zero Frequencies -- Processes Defined in Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Multiple Spectrum Peaks -- Randomized Harmonic Model -- Randomized Harmonic Processes with One Spectrum Peak -- Randomized Harmonic Processes with Multiple Spectrum Peaks -- Monte Carlo Simulation of Randomized Harmonic Processes -- Generation of Two Correlated Gaussian Processes -- Method of Linear Filters -- Two Correlated Gaussian Random Variables -- Two Correlated Gaussian White Noises -- Two Correlated Gaussian Processes -- Series Expansion with Random Amplitudes -- Series Expansion with Random Phases -- Conclusion -- References -- Chapter 4Estimation Problems for Periodically CorrelatedStochastic Sequences with Missed Observations -- Abstract -- 1. Introduction -- 2. Periodically Correlated Sequences and MultidimensionalStationary Sequences -- 3. The Hilbert Space ProjectionMethod of Extrapolationof Functionals -- 3.1. Extrapolation of Functionals from Observations without Noise -- 3.2. Extrapolation of Finite Sum Functionals -- 4. Minimax (Robust) Method of Linear Extrapolation -- 4.1. The Least Favorable Spectral Densities in the Class D = D0 × DU -- 4.2. The Least Favorable Spectral Densities in the Class D = D" × D -- 5. The Hilbert Space ProjectionMethod of Interpolationof Functionals -- 5.1. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 1 -- 5.2. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 2. 6. Minimax (Robust) Method of Linear Interpolation -- 6.1. The Least Favorable Spectral Densities in D− -- 6.2. The Least Favorable Spectral Densities in D− -- Conclusion -- References -- Chapter 5Coupling Method in Studying Stabilityof Time-InhomogeneousMarkov Chains -- Abstract -- 1. Introduction -- 2. Coupling of Two Chains -- 3. UniformMinorization Case -- 4. Relaxing the Proximity Condition -- 5. Nonuniform Minorization -- 6. Renewal Process Generated by a Pair of InhomogeneousMarkov Chains -- 6.1. Dependence of Renewal Moments for Time-InhomogeneousMarkov Chain -- 6.2. Key Definitions -- 6.3. Formal Definition of the l(t) Variable -- Conclusion -- References -- Chapter 6Minimax Prediction of Sequences with PeriodicallyStationary Increments Observed with Noise andCointegrated Sequences -- Abstract -- 1. Introduction -- 2. Stochastic Sequences with Periodically StationaryIncrements -- 3. Hilbert Space ProjectionMethod of Prediction -- 3.1. Prediction of Vector-Valued Stochastic Sequences withStationary Increments -- 3.2. Prediction Based on Factorizations of the Spectral Densities -- 3.3. Prediction of Stochastic Sequences with Periodically StationaryIncrement -- 3.4. Prediction of One Class of Cointegrated Vector Stochastic Sequences -- 4. Minimax (Robust) Method of Prediction -- 4.1. Least Favorable Spectral Density in Classes D0 × D1 -- 4.2. Least Favorable Spectral Density in Classes D0 × D1 for CointegratedVector Sequences -- 4.3. Least Favorable Spectral Density in Classes D" × DU -- 4.4. Least Favorable Spectral Density for Cointegrated Vector Sequences inClasses D" × DU -- Conclusion -- References -- Chapter 7Estimation of Multidimensional Stationary StochasticSequences from Observations in Special Sets of Points -- Abstract -- 1. Introduction -- 2. The Hilbert Space ProjectionMethod of LinearEstimation. 3. Minimax-RobustMethod of Interpolation -- 4. Least Favourable Spectral Densities in the Class D0,0 -- 5. Least Favourable Spectral Densities in Classes DUV × D -- 6. Least Favourable Spectral Densities in Classes D1"1 × D2"2 -- 7. Least Favourable Spectral Densities in the Class D− -- 8. Least Favourable Spectral Densities in the Class DW -- 9. Least Favourable Spectral Densities in the Class DU -- Conclusion -- References -- Chapter 8Invariant Measures and Asymptotic Behavior ofStochastic Evolution Equations -- Abstract -- 1. Introduction -- 2. Bounded Solutions and InvariantMeasures inWeighted Spaces -- 2.1. Strong Dissipation: Exponentially Contractive Semigroup -- 2.2. Weak Dissipation -- 2.2.1. Proof of Theorem 8. Preliminary Facts -- 2.2.2. Ito's Formula -- 2.2.3. The Relation between Ito's Formula and Weak Solutions -- 3. Asymptotic Results for Invariant Measures -- 3.1. Vanishing Dissipation Limit -- 3.2. Homogenization -- 3.2.1. Homogenization Notation and Preliminaries -- 3.2.2. Nash-Aranson Estimates. Semigroup Estimates -- 3.2.3. Proof of Theorem 14 -- 4. Existence of InvariantMeasure for SPDEs withNon-Lipschitz Coefficients -- 4.1. Existence of InvariantMeasure -- 4.2. Uniquences of InvariantMeasure -- 4.3. Examples. -- 4.3.1. Local Elliptic Operator -- 4.3.2. Nonlocal Elliptic Operator -- 4.3.3. Allen-Cahn Nonlinearity -- Conclusion -- Acknowledgments -- References -- Chapter 9Quasi-Banach Spaces of Random Variables andModeling of Stochastic Processes -- Abstract -- 1. Introduction -- 2. Pre-Banach Spaces DV,W of Random Variables -- 2.1. Basic Definitions -- 2.2. Spaces DV,W() of Random Variables -- 2.3. Convergence of Series in the Spaces DV,W(). -- 2.4. Convergence of Infinite Sums of Random Variables withSpecific Distributionsin the Space DV,W -- 2.5. Stochastic Processes in the Space DV,W. 2.6. Boundedness of the Supremumof Stochastic Processes in the SpaceDV,W -- 2.7. Continuity of stochastic processes belonging to the spaces DV,W -- 2.8. Uniform Convergence of Function Series in DV,W -- 2.9. Models of Stochastic Processes from the Space DV,W -- 2.10. Examples of Models of Stochastic Processes from the Space DV,W() -- 3. Modeling of Stochastic Processes in Lp(T) UsingApproximated Decompositions -- 3.1. Basic Definitions -- 3.2. Modeling of Stochastic Processes in Lp(T ) Using OrthogonalPolynomials -- 3.3. Modeling of Stochastic Processes in Lp(0, T ) Using the HermitePolynomials -- 3.4. Modeling of Stochastic Processes in Lp(0, T ) Using the ChebyshevPolynomials -- 4. Models of '-Sub-Gaussian Stochastic Processes in C(T)Spaces -- 4.1. Models of Stochastic Processes in C(T ) That Allow Representation inSeries with Independent Elements -- Conclusion -- References -- Chapter 10Simulation of Stochastic Processes with GivenReliability and Accuracy -- Abstract -- 1. Introduction -- 2. Simulation of Stationary Random Sequences -- 2.1. Basic Definitions -- 2.2. Spectral Decomposition of Stationary Random Sequence -- 2.3. '-Sub-Gaussian Random Variables -- 2.4. Main Results of the Section 2 -- 2.5. The Case Study -- 2.5.1. The AR(1) Sequence -- 2.5.2. The ARMA(1,1) Sequence -- 3. Methods of StatisticalModeling of StochasticProcesses Represented in the Form of Series -- 3.1. Convergence of Strictly Sub-Gaussian Random Series in L2(T ) -- 3.2. Accuracy and Reliability of StatisticalModeling of Sub-GaussianHomogeneous Random Fields on a Sphere -- 4. Simulation of Stochastic Processes as Input on a System Tak-ing into Account the System Response -- 4.1. Space of Square-Gaussian Random Variables and Square-GaussianStochastic Processes -- 4.2. The Distribution of Supremums of Square-Gaussian StochasticProcesses. Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Stochastic processes Mathematical models. Processus stochastiques. Processus stochastiques Modèles mathématiques. Stochastic processes fast Stochastic processes Mathematical models fast Moklyachuk, Mikhail P., editor. Print version: Stochastic processes New York : Nova Science Publishers, [2023] 9781685079826 (DLC) 2022057363 |
| spellingShingle | Stochastic processes : fundamentals and emerging applications / Intro -- Stochastic ProcessesFundamentals and Emerging Applications -- Contents -- Preface -- Chapter 1Asymptotic Behavior of Extreme Values of RandomVariables and Some Stochastic Processes -- Abstract -- 1. Introduction -- 2. Asymptotic Behavior of Extreme Values ofRandom Variables -- 2.1. Some Early Results -- 2.2. Law of the Iterated Logarithm and a Law of the Triple Logarithm andIts Generalization -- 2.3. "Confidence Intervals" for Extrema of Discrete Random Variables -- 3. Asymptotic Behavior of Extreme Valuesof Regenerative Processes -- 3.1. General Regenerative Processes -- 3.2. Birth and Death Processes -- 3.3. Processes in Queuing Systems -- Conclusion -- References -- Chapter 2Long-Time Behavior of Stochastic Models ofPopulation Dynamics with Jumps -- Abstract -- 1. Introduction -- 2. Stochastic Non-Autonomous Logistic Modelswith Jumps -- 2.1. Definitions and Notations -- 2.2. Non-Autonomous Stochastic Logistic Differential Equation with LinearRandom Perturbations -- 2.3. Logistic Model with Periodical Coefficients -- 2.4. Related Stochastic Differential Equation -- 2.5. Non-Autonomous Stochastic Logistic Differential Equation withNon-Linear Random Perturbations -- 3. Stochastic Two-SpeciesMutualism Model with Jumps -- 3.1. Notations and Definitions -- 3.2. Long-Time Behavior of StochasticMutualismModel -- 4. A Non-Autonomous Stochastic Predator-PreyModelswith Jumps -- 4.1. A Non-Autonomous Predator-Prey Model with a Modified Versionof Leslie-Gower Term and Holling-Type II Functional Response -- 4.2. A Predator-Prey Model with Beddington-DeAngelis FunctionalResponse -- Conclusion -- References -- Chapter 3Modeling and Simulation of Stochastic Processes -- Abstract -- Introduction -- Generation of a Gaussian Process -- Method of Linear Filters -- Gaussian White Noise -- Linear Filters -- Series Expansion with Random Amplitudes. Series Expansion with Random Phases -- Series Expansion with Random Amplitudes and Random Phases -- Generation of a Non-Gaussian Process -- Method of Nonlinear Filters -- Low-Pass Processes -- Processes Defined in Infinite Interval -- Processes Defined in Semi-Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Spectrum Peaks at Non-Zero Frequencies -- Processes Defined in Infinite Interval -- Processes Defined in Finite Intervals -- Processes with Multiple Spectrum Peaks -- Randomized Harmonic Model -- Randomized Harmonic Processes with One Spectrum Peak -- Randomized Harmonic Processes with Multiple Spectrum Peaks -- Monte Carlo Simulation of Randomized Harmonic Processes -- Generation of Two Correlated Gaussian Processes -- Method of Linear Filters -- Two Correlated Gaussian Random Variables -- Two Correlated Gaussian White Noises -- Two Correlated Gaussian Processes -- Series Expansion with Random Amplitudes -- Series Expansion with Random Phases -- Conclusion -- References -- Chapter 4Estimation Problems for Periodically CorrelatedStochastic Sequences with Missed Observations -- Abstract -- 1. Introduction -- 2. Periodically Correlated Sequences and MultidimensionalStationary Sequences -- 3. The Hilbert Space ProjectionMethod of Extrapolationof Functionals -- 3.1. Extrapolation of Functionals from Observations without Noise -- 3.2. Extrapolation of Finite Sum Functionals -- 4. Minimax (Robust) Method of Linear Extrapolation -- 4.1. The Least Favorable Spectral Densities in the Class D = D0 × DU -- 4.2. The Least Favorable Spectral Densities in the Class D = D" × D -- 5. The Hilbert Space ProjectionMethod of Interpolationof Functionals -- 5.1. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 1 -- 5.2. Interpolation of T-PC Stochastic Sequences with Special Sets of MissedObservations. 2. 6. Minimax (Robust) Method of Linear Interpolation -- 6.1. The Least Favorable Spectral Densities in D− -- 6.2. The Least Favorable Spectral Densities in D− -- Conclusion -- References -- Chapter 5Coupling Method in Studying Stabilityof Time-InhomogeneousMarkov Chains -- Abstract -- 1. Introduction -- 2. Coupling of Two Chains -- 3. UniformMinorization Case -- 4. Relaxing the Proximity Condition -- 5. Nonuniform Minorization -- 6. Renewal Process Generated by a Pair of InhomogeneousMarkov Chains -- 6.1. Dependence of Renewal Moments for Time-InhomogeneousMarkov Chain -- 6.2. Key Definitions -- 6.3. Formal Definition of the l(t) Variable -- Conclusion -- References -- Chapter 6Minimax Prediction of Sequences with PeriodicallyStationary Increments Observed with Noise andCointegrated Sequences -- Abstract -- 1. Introduction -- 2. Stochastic Sequences with Periodically StationaryIncrements -- 3. Hilbert Space ProjectionMethod of Prediction -- 3.1. Prediction of Vector-Valued Stochastic Sequences withStationary Increments -- 3.2. Prediction Based on Factorizations of the Spectral Densities -- 3.3. Prediction of Stochastic Sequences with Periodically StationaryIncrement -- 3.4. Prediction of One Class of Cointegrated Vector Stochastic Sequences -- 4. Minimax (Robust) Method of Prediction -- 4.1. Least Favorable Spectral Density in Classes D0 × D1 -- 4.2. Least Favorable Spectral Density in Classes D0 × D1 for CointegratedVector Sequences -- 4.3. Least Favorable Spectral Density in Classes D" × DU -- 4.4. Least Favorable Spectral Density for Cointegrated Vector Sequences inClasses D" × DU -- Conclusion -- References -- Chapter 7Estimation of Multidimensional Stationary StochasticSequences from Observations in Special Sets of Points -- Abstract -- 1. Introduction -- 2. The Hilbert Space ProjectionMethod of LinearEstimation. 3. Minimax-RobustMethod of Interpolation -- 4. Least Favourable Spectral Densities in the Class D0,0 -- 5. Least Favourable Spectral Densities in Classes DUV × D -- 6. Least Favourable Spectral Densities in Classes D1"1 × D2"2 -- 7. Least Favourable Spectral Densities in the Class D− -- 8. Least Favourable Spectral Densities in the Class DW -- 9. Least Favourable Spectral Densities in the Class DU -- Conclusion -- References -- Chapter 8Invariant Measures and Asymptotic Behavior ofStochastic Evolution Equations -- Abstract -- 1. Introduction -- 2. Bounded Solutions and InvariantMeasures inWeighted Spaces -- 2.1. Strong Dissipation: Exponentially Contractive Semigroup -- 2.2. Weak Dissipation -- 2.2.1. Proof of Theorem 8. Preliminary Facts -- 2.2.2. Ito's Formula -- 2.2.3. The Relation between Ito's Formula and Weak Solutions -- 3. Asymptotic Results for Invariant Measures -- 3.1. Vanishing Dissipation Limit -- 3.2. Homogenization -- 3.2.1. Homogenization Notation and Preliminaries -- 3.2.2. Nash-Aranson Estimates. Semigroup Estimates -- 3.2.3. Proof of Theorem 14 -- 4. Existence of InvariantMeasure for SPDEs withNon-Lipschitz Coefficients -- 4.1. Existence of InvariantMeasure -- 4.2. Uniquences of InvariantMeasure -- 4.3. Examples. -- 4.3.1. Local Elliptic Operator -- 4.3.2. Nonlocal Elliptic Operator -- 4.3.3. Allen-Cahn Nonlinearity -- Conclusion -- Acknowledgments -- References -- Chapter 9Quasi-Banach Spaces of Random Variables andModeling of Stochastic Processes -- Abstract -- 1. Introduction -- 2. Pre-Banach Spaces DV,W of Random Variables -- 2.1. Basic Definitions -- 2.2. Spaces DV,W() of Random Variables -- 2.3. Convergence of Series in the Spaces DV,W(). -- 2.4. Convergence of Infinite Sums of Random Variables withSpecific Distributionsin the Space DV,W -- 2.5. Stochastic Processes in the Space DV,W. 2.6. Boundedness of the Supremumof Stochastic Processes in the SpaceDV,W -- 2.7. Continuity of stochastic processes belonging to the spaces DV,W -- 2.8. Uniform Convergence of Function Series in DV,W -- 2.9. Models of Stochastic Processes from the Space DV,W -- 2.10. Examples of Models of Stochastic Processes from the Space DV,W() -- 3. Modeling of Stochastic Processes in Lp(T) UsingApproximated Decompositions -- 3.1. Basic Definitions -- 3.2. Modeling of Stochastic Processes in Lp(T ) Using OrthogonalPolynomials -- 3.3. Modeling of Stochastic Processes in Lp(0, T ) Using the HermitePolynomials -- 3.4. Modeling of Stochastic Processes in Lp(0, T ) Using the ChebyshevPolynomials -- 4. Models of '-Sub-Gaussian Stochastic Processes in C(T)Spaces -- 4.1. Models of Stochastic Processes in C(T ) That Allow Representation inSeries with Independent Elements -- Conclusion -- References -- Chapter 10Simulation of Stochastic Processes with GivenReliability and Accuracy -- Abstract -- 1. Introduction -- 2. Simulation of Stationary Random Sequences -- 2.1. Basic Definitions -- 2.2. Spectral Decomposition of Stationary Random Sequence -- 2.3. '-Sub-Gaussian Random Variables -- 2.4. Main Results of the Section 2 -- 2.5. The Case Study -- 2.5.1. The AR(1) Sequence -- 2.5.2. The ARMA(1,1) Sequence -- 3. Methods of StatisticalModeling of StochasticProcesses Represented in the Form of Series -- 3.1. Convergence of Strictly Sub-Gaussian Random Series in L2(T ) -- 3.2. Accuracy and Reliability of StatisticalModeling of Sub-GaussianHomogeneous Random Fields on a Sphere -- 4. Simulation of Stochastic Processes as Input on a System Tak-ing into Account the System Response -- 4.1. Space of Square-Gaussian Random Variables and Square-GaussianStochastic Processes -- 4.2. The Distribution of Supremums of Square-Gaussian StochasticProcesses. Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Stochastic processes Mathematical models. Processus stochastiques. Processus stochastiques Modèles mathématiques. Stochastic processes fast Stochastic processes Mathematical models fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85128181 |
| title | Stochastic processes : fundamentals and emerging applications / |
| title_auth | Stochastic processes : fundamentals and emerging applications / |
| title_exact_search | Stochastic processes : fundamentals and emerging applications / |
| title_full | Stochastic processes : fundamentals and emerging applications / Mikhail Moklyachuk, D.Sci. (editor), Professor, Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. |
| title_fullStr | Stochastic processes : fundamentals and emerging applications / Mikhail Moklyachuk, D.Sci. (editor), Professor, Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. |
| title_full_unstemmed | Stochastic processes : fundamentals and emerging applications / Mikhail Moklyachuk, D.Sci. (editor), Professor, Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. |
| title_short | Stochastic processes : |
| title_sort | stochastic processes fundamentals and emerging applications |
| title_sub | fundamentals and emerging applications / |
| topic | Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Stochastic processes Mathematical models. Processus stochastiques. Processus stochastiques Modèles mathématiques. Stochastic processes fast Stochastic processes Mathematical models fast |
| topic_facet | Stochastic processes. Stochastic processes Mathematical models. Processus stochastiques. Processus stochastiques Modèles mathématiques. Stochastic processes Stochastic processes Mathematical models |
| work_keys_str_mv | AT moklyachukmikhailp stochasticprocessesfundamentalsandemergingapplications |