Stochastic systems in merging phase space /:
This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numericall...
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| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore ; Hackensack, NJ :
World Scientific,
©2005.
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| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book. |
| Physical Description: | 1 online resource (xv, 331 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 315-323) and index. |
| ISBN: | 9812565914 9789812565914 9812703128 9789812703125 1281899119 9781281899118 9786611899110 6611899111 |
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MARC
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| 100 | 1 | |a Koroli︠u︡k, V. S. |q (Vladimir Semenovich), |d 1925- |1 https://id.oclc.org/worldcat/entity/E39PBJtmth7FXvvRKtjrcb6VG3 |0 http://id.loc.gov/authorities/names/n81087114 | |
| 245 | 1 | 0 | |a Stochastic systems in merging phase space / |c Vladimir S. Koroliuk, Nikolas Limnios. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2005. | ||
| 300 | |a 1 online resource (xv, 331 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 504 | |a Includes bibliographical references (pages 315-323) and index. | ||
| 505 | 0 | |a Cover -- Preface -- Contents -- 1. Markov and Semi-Markov Processes -- 1.1 Preliminaries -- 1.2 Markov Processes -- 1.2.1 Markov Chains -- 1.2.2 Continuous-Time Markov Processes -- 1.2.3 Diffusion Processes -- 1.2.4 Processes with Independent Increments -- 1.2.5 Processes with Locally Independent Increments -- 1.2.6 Martingale Characterization of Markov Processes -- 1.3 Semi-Markov Processes -- 1.3.1 Markov Renewal Processes -- 1.3.2 Markov Renewal Equation and Theorem -- 1.3.3 Auxiliary Processes -- 1.3.4 Compensating Operators -- 1.3.5 Martingale Characterization of Markov Renewal Processes -- 1.4 Semimartingales -- 1.5 Counting Markov Renewal Processes -- 1.6 Reducible-Invertible Operators -- 2. Stochastic Systems with Switching -- 2.1 Introduction -- 2.2 Stochastic Integral Functionals -- 2.3 Increment Processes -- 2.4 Stochastic Evolutionary Systems -- 2.5 Markov Additive Processes -- 2.6 Stochastic Additive Functionals -- 2.7 Random Evolutions -- 2.7.1 Continuous Random Evolutions -- 2.7.2 Jump Random Evolutions -- 2.7.3 Semi-Markov Random Evolutions -- 2.8 Extended Compensating Operators -- 2.9 Markov Additive Semimartingales -- 2.9.1 Impulsive Processes -- 2.9.2 Continuous Predictable Characteristics -- 3. Stochastic Systems in the Series Scheme -- 3.1 Introduction -- 3.2 Random Evolutions in the Series Scheme -- 3.2.1 Continuous Random Evolutions -- 3.2.2 Jump Random Evolutions -- 3.3 Average Approximation -- 3.3.1 Stochastic Additive Functionals -- 3.3.2 Increment Processes -- 3.4 Diffusion Approximation -- 3.4.1 Stochastic Integral Functionals -- 3.4.2 Stochastic Additive Functionals -- 3.4.3 Stochastic Evolutionary Systems -- 3.4.4 Increment Processes -- 3.5 Diffusion Approximation with Equilibrium -- 3.5.1 Locally Independent Increment Processes -- 3.5.2 Stochastic Additive Functionals with Equilibrium -- 3.5.3 Stochastic Evolutionary Systems with Semi-Markov Switching -- 4. Stochastic Systems with Split and Merging -- 4.1 Introduction -- 4.2 Phase Merging Scheme -- 4.2.1 Ergodic Merging -- 4.2.2 Merging with Absorption -- 4.2.3 Ergodic Double Merging -- 4.3 Average with Merging -- 4.3.1 Ergodic Average -- 4.3.2 Average with Absorption -- 4.3.3 Ergodic Average with Double Merging -- 4.3.4 Double Average with Absorption -- 4.4 Diffusion Approximation with Split and Merging -- 4.4.1 Ergodic Split and Merging -- 4.4.2 Split and Merging with Absorption -- 4.4.3 Ergodic Split and Double Merging -- 4.4.4 Double Split and Merging -- 4.4.5 Double Split and Double Merging -- 4.5 Integral F'unctionals in Split Phase Space -- 4.5.1 Ergodic Split -- 4.5.2 Double Split and Merging -- 4.5.3 Triple Split and Merging -- 5. Phase Merging Principles -- 5.1 Introduction -- 5.2 Perturbation of Reducible-Invertible Operators -- 5.2.1 Preliminaries -- 5.2.2 Solution of Singular Perturbation Problems -- 5.3 Average Merging Principle -- 5.3.1 Stochastic Evolutionary Systems -- 5.3.2 Stochastic Additive F'unctionals -- 5.3.3 Increment Processes -- 5.3.4 Continuous Random Evolutions -- 5.3.5 Jump Random Evolutions -- 5.3.6 Random Evolutions with Markov Switching -- 5.4 Diffusion Approximation Principle -- 5.4.1 Stochastic Integral F'unctionals -- 5.4.2 Continuous Random Evolutions -- 5.4.3 Jump Random Evolution. | |
| 520 | |a This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Stochastic processes. |0 http://id.loc.gov/authorities/subjects/sh85128181 | |
| 650 | 0 | |a Mathematical optimization. |0 http://id.loc.gov/authorities/subjects/sh85082127 | |
| 650 | 2 | |a Stochastic Processes |0 https://id.nlm.nih.gov/mesh/D013269 | |
| 650 | 6 | |a Processus stochastiques. | |
| 650 | 6 | |a Optimisation mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a Mathematical optimization |2 fast | |
| 650 | 7 | |a Stochastic processes |2 fast | |
| 655 | 0 | |a Electronic books. | |
| 700 | 1 | |a Limnios, N. |q (Nikolaos) |1 https://id.oclc.org/worldcat/entity/E39PBJbGVrtdQxWvdtVWMKkFKd |0 http://id.loc.gov/authorities/names/n98057246 | |
| 776 | 0 | 8 | |i Print version: |a Koroli︠u︡k, V.S. (Vladimir Semenovich), 1925- |t Stochastic systems in merging phase space. |d Singapore ; Hackensack, NJ : World Scientific, ©2005 |w (DLC) 2006283982 |
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| author | Koroli︠u︡k, V. S. (Vladimir Semenovich), 1925- |
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| contents | Cover -- Preface -- Contents -- 1. Markov and Semi-Markov Processes -- 1.1 Preliminaries -- 1.2 Markov Processes -- 1.2.1 Markov Chains -- 1.2.2 Continuous-Time Markov Processes -- 1.2.3 Diffusion Processes -- 1.2.4 Processes with Independent Increments -- 1.2.5 Processes with Locally Independent Increments -- 1.2.6 Martingale Characterization of Markov Processes -- 1.3 Semi-Markov Processes -- 1.3.1 Markov Renewal Processes -- 1.3.2 Markov Renewal Equation and Theorem -- 1.3.3 Auxiliary Processes -- 1.3.4 Compensating Operators -- 1.3.5 Martingale Characterization of Markov Renewal Processes -- 1.4 Semimartingales -- 1.5 Counting Markov Renewal Processes -- 1.6 Reducible-Invertible Operators -- 2. Stochastic Systems with Switching -- 2.1 Introduction -- 2.2 Stochastic Integral Functionals -- 2.3 Increment Processes -- 2.4 Stochastic Evolutionary Systems -- 2.5 Markov Additive Processes -- 2.6 Stochastic Additive Functionals -- 2.7 Random Evolutions -- 2.7.1 Continuous Random Evolutions -- 2.7.2 Jump Random Evolutions -- 2.7.3 Semi-Markov Random Evolutions -- 2.8 Extended Compensating Operators -- 2.9 Markov Additive Semimartingales -- 2.9.1 Impulsive Processes -- 2.9.2 Continuous Predictable Characteristics -- 3. Stochastic Systems in the Series Scheme -- 3.1 Introduction -- 3.2 Random Evolutions in the Series Scheme -- 3.2.1 Continuous Random Evolutions -- 3.2.2 Jump Random Evolutions -- 3.3 Average Approximation -- 3.3.1 Stochastic Additive Functionals -- 3.3.2 Increment Processes -- 3.4 Diffusion Approximation -- 3.4.1 Stochastic Integral Functionals -- 3.4.2 Stochastic Additive Functionals -- 3.4.3 Stochastic Evolutionary Systems -- 3.4.4 Increment Processes -- 3.5 Diffusion Approximation with Equilibrium -- 3.5.1 Locally Independent Increment Processes -- 3.5.2 Stochastic Additive Functionals with Equilibrium -- 3.5.3 Stochastic Evolutionary Systems with Semi-Markov Switching -- 4. Stochastic Systems with Split and Merging -- 4.1 Introduction -- 4.2 Phase Merging Scheme -- 4.2.1 Ergodic Merging -- 4.2.2 Merging with Absorption -- 4.2.3 Ergodic Double Merging -- 4.3 Average with Merging -- 4.3.1 Ergodic Average -- 4.3.2 Average with Absorption -- 4.3.3 Ergodic Average with Double Merging -- 4.3.4 Double Average with Absorption -- 4.4 Diffusion Approximation with Split and Merging -- 4.4.1 Ergodic Split and Merging -- 4.4.2 Split and Merging with Absorption -- 4.4.3 Ergodic Split and Double Merging -- 4.4.4 Double Split and Merging -- 4.4.5 Double Split and Double Merging -- 4.5 Integral F'unctionals in Split Phase Space -- 4.5.1 Ergodic Split -- 4.5.2 Double Split and Merging -- 4.5.3 Triple Split and Merging -- 5. Phase Merging Principles -- 5.1 Introduction -- 5.2 Perturbation of Reducible-Invertible Operators -- 5.2.1 Preliminaries -- 5.2.2 Solution of Singular Perturbation Problems -- 5.3 Average Merging Principle -- 5.3.1 Stochastic Evolutionary Systems -- 5.3.2 Stochastic Additive F'unctionals -- 5.3.3 Increment Processes -- 5.3.4 Continuous Random Evolutions -- 5.3.5 Jump Random Evolutions -- 5.3.6 Random Evolutions with Markov Switching -- 5.4 Diffusion Approximation Principle -- 5.4.1 Stochastic Integral F'unctionals -- 5.4.2 Continuous Random Evolutions -- 5.4.3 Jump Random Evolution. |
| ctrlnum | (OCoLC)228172388 |
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| 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 |
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Koroliuk, Nikolas Limnios.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">Hackensack, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2005.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xv, 331 pages) :</subfield><subfield code="b">illustrations</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="347" ind1=" " ind2=" "><subfield code="a">data file</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 315-323) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover -- Preface -- Contents -- 1. Markov and Semi-Markov Processes -- 1.1 Preliminaries -- 1.2 Markov Processes -- 1.2.1 Markov Chains -- 1.2.2 Continuous-Time Markov Processes -- 1.2.3 Diffusion Processes -- 1.2.4 Processes with Independent Increments -- 1.2.5 Processes with Locally Independent Increments -- 1.2.6 Martingale Characterization of Markov Processes -- 1.3 Semi-Markov Processes -- 1.3.1 Markov Renewal Processes -- 1.3.2 Markov Renewal Equation and Theorem -- 1.3.3 Auxiliary Processes -- 1.3.4 Compensating Operators -- 1.3.5 Martingale Characterization of Markov Renewal Processes -- 1.4 Semimartingales -- 1.5 Counting Markov Renewal Processes -- 1.6 Reducible-Invertible Operators -- 2. Stochastic Systems with Switching -- 2.1 Introduction -- 2.2 Stochastic Integral Functionals -- 2.3 Increment Processes -- 2.4 Stochastic Evolutionary Systems -- 2.5 Markov Additive Processes -- 2.6 Stochastic Additive Functionals -- 2.7 Random Evolutions -- 2.7.1 Continuous Random Evolutions -- 2.7.2 Jump Random Evolutions -- 2.7.3 Semi-Markov Random Evolutions -- 2.8 Extended Compensating Operators -- 2.9 Markov Additive Semimartingales -- 2.9.1 Impulsive Processes -- 2.9.2 Continuous Predictable Characteristics -- 3. Stochastic Systems in the Series Scheme -- 3.1 Introduction -- 3.2 Random Evolutions in the Series Scheme -- 3.2.1 Continuous Random Evolutions -- 3.2.2 Jump Random Evolutions -- 3.3 Average Approximation -- 3.3.1 Stochastic Additive Functionals -- 3.3.2 Increment Processes -- 3.4 Diffusion Approximation -- 3.4.1 Stochastic Integral Functionals -- 3.4.2 Stochastic Additive Functionals -- 3.4.3 Stochastic Evolutionary Systems -- 3.4.4 Increment Processes -- 3.5 Diffusion Approximation with Equilibrium -- 3.5.1 Locally Independent Increment Processes -- 3.5.2 Stochastic Additive Functionals with Equilibrium -- 3.5.3 Stochastic Evolutionary Systems with Semi-Markov Switching -- 4. Stochastic Systems with Split and Merging -- 4.1 Introduction -- 4.2 Phase Merging Scheme -- 4.2.1 Ergodic Merging -- 4.2.2 Merging with Absorption -- 4.2.3 Ergodic Double Merging -- 4.3 Average with Merging -- 4.3.1 Ergodic Average -- 4.3.2 Average with Absorption -- 4.3.3 Ergodic Average with Double Merging -- 4.3.4 Double Average with Absorption -- 4.4 Diffusion Approximation with Split and Merging -- 4.4.1 Ergodic Split and Merging -- 4.4.2 Split and Merging with Absorption -- 4.4.3 Ergodic Split and Double Merging -- 4.4.4 Double Split and Merging -- 4.4.5 Double Split and Double Merging -- 4.5 Integral F'unctionals in Split Phase Space -- 4.5.1 Ergodic Split -- 4.5.2 Double Split and Merging -- 4.5.3 Triple Split and Merging -- 5. Phase Merging Principles -- 5.1 Introduction -- 5.2 Perturbation of Reducible-Invertible Operators -- 5.2.1 Preliminaries -- 5.2.2 Solution of Singular Perturbation Problems -- 5.3 Average Merging Principle -- 5.3.1 Stochastic Evolutionary Systems -- 5.3.2 Stochastic Additive F'unctionals -- 5.3.3 Increment Processes -- 5.3.4 Continuous Random Evolutions -- 5.3.5 Jump Random Evolutions -- 5.3.6 Random Evolutions with Markov Switching -- 5.4 Diffusion Approximation Principle -- 5.4.1 Stochastic Integral F'unctionals -- 5.4.2 Continuous Random Evolutions -- 5.4.3 Jump Random Evolution.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. 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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn228172388 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:36:04Z |
| institution | BVB |
| isbn | 9812565914 9789812565914 9812703128 9789812703125 1281899119 9781281899118 9786611899110 6611899111 |
| language | English |
| oclc_num | 228172388 |
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| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 331 pages) : illustrations |
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| publisher | World Scientific, |
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| spelling | Koroli︠u︡k, V. S. (Vladimir Semenovich), 1925- https://id.oclc.org/worldcat/entity/E39PBJtmth7FXvvRKtjrcb6VG3 http://id.loc.gov/authorities/names/n81087114 Stochastic systems in merging phase space / Vladimir S. Koroliuk, Nikolas Limnios. Singapore ; Hackensack, NJ : World Scientific, ©2005. 1 online resource (xv, 331 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 315-323) and index. Cover -- Preface -- Contents -- 1. Markov and Semi-Markov Processes -- 1.1 Preliminaries -- 1.2 Markov Processes -- 1.2.1 Markov Chains -- 1.2.2 Continuous-Time Markov Processes -- 1.2.3 Diffusion Processes -- 1.2.4 Processes with Independent Increments -- 1.2.5 Processes with Locally Independent Increments -- 1.2.6 Martingale Characterization of Markov Processes -- 1.3 Semi-Markov Processes -- 1.3.1 Markov Renewal Processes -- 1.3.2 Markov Renewal Equation and Theorem -- 1.3.3 Auxiliary Processes -- 1.3.4 Compensating Operators -- 1.3.5 Martingale Characterization of Markov Renewal Processes -- 1.4 Semimartingales -- 1.5 Counting Markov Renewal Processes -- 1.6 Reducible-Invertible Operators -- 2. Stochastic Systems with Switching -- 2.1 Introduction -- 2.2 Stochastic Integral Functionals -- 2.3 Increment Processes -- 2.4 Stochastic Evolutionary Systems -- 2.5 Markov Additive Processes -- 2.6 Stochastic Additive Functionals -- 2.7 Random Evolutions -- 2.7.1 Continuous Random Evolutions -- 2.7.2 Jump Random Evolutions -- 2.7.3 Semi-Markov Random Evolutions -- 2.8 Extended Compensating Operators -- 2.9 Markov Additive Semimartingales -- 2.9.1 Impulsive Processes -- 2.9.2 Continuous Predictable Characteristics -- 3. Stochastic Systems in the Series Scheme -- 3.1 Introduction -- 3.2 Random Evolutions in the Series Scheme -- 3.2.1 Continuous Random Evolutions -- 3.2.2 Jump Random Evolutions -- 3.3 Average Approximation -- 3.3.1 Stochastic Additive Functionals -- 3.3.2 Increment Processes -- 3.4 Diffusion Approximation -- 3.4.1 Stochastic Integral Functionals -- 3.4.2 Stochastic Additive Functionals -- 3.4.3 Stochastic Evolutionary Systems -- 3.4.4 Increment Processes -- 3.5 Diffusion Approximation with Equilibrium -- 3.5.1 Locally Independent Increment Processes -- 3.5.2 Stochastic Additive Functionals with Equilibrium -- 3.5.3 Stochastic Evolutionary Systems with Semi-Markov Switching -- 4. Stochastic Systems with Split and Merging -- 4.1 Introduction -- 4.2 Phase Merging Scheme -- 4.2.1 Ergodic Merging -- 4.2.2 Merging with Absorption -- 4.2.3 Ergodic Double Merging -- 4.3 Average with Merging -- 4.3.1 Ergodic Average -- 4.3.2 Average with Absorption -- 4.3.3 Ergodic Average with Double Merging -- 4.3.4 Double Average with Absorption -- 4.4 Diffusion Approximation with Split and Merging -- 4.4.1 Ergodic Split and Merging -- 4.4.2 Split and Merging with Absorption -- 4.4.3 Ergodic Split and Double Merging -- 4.4.4 Double Split and Merging -- 4.4.5 Double Split and Double Merging -- 4.5 Integral F'unctionals in Split Phase Space -- 4.5.1 Ergodic Split -- 4.5.2 Double Split and Merging -- 4.5.3 Triple Split and Merging -- 5. Phase Merging Principles -- 5.1 Introduction -- 5.2 Perturbation of Reducible-Invertible Operators -- 5.2.1 Preliminaries -- 5.2.2 Solution of Singular Perturbation Problems -- 5.3 Average Merging Principle -- 5.3.1 Stochastic Evolutionary Systems -- 5.3.2 Stochastic Additive F'unctionals -- 5.3.3 Increment Processes -- 5.3.4 Continuous Random Evolutions -- 5.3.5 Jump Random Evolutions -- 5.3.6 Random Evolutions with Markov Switching -- 5.4 Diffusion Approximation Principle -- 5.4.1 Stochastic Integral F'unctionals -- 5.4.2 Continuous Random Evolutions -- 5.4.3 Jump Random Evolution. This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asymptotic split and merging schemes. Most of the results from semi-Markov processes are new and presented for the first time in this book. Print version record. English. Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Processus stochastiques. Optimisation mathématique. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Mathematical optimization fast Stochastic processes fast Electronic books. Limnios, N. (Nikolaos) https://id.oclc.org/worldcat/entity/E39PBJbGVrtdQxWvdtVWMKkFKd http://id.loc.gov/authorities/names/n98057246 Print version: Koroli︠u︡k, V.S. (Vladimir Semenovich), 1925- Stochastic systems in merging phase space. Singapore ; Hackensack, NJ : World Scientific, ©2005 (DLC) 2006283982 |
| spellingShingle | Koroli︠u︡k, V. S. (Vladimir Semenovich), 1925- Stochastic systems in merging phase space / Cover -- Preface -- Contents -- 1. Markov and Semi-Markov Processes -- 1.1 Preliminaries -- 1.2 Markov Processes -- 1.2.1 Markov Chains -- 1.2.2 Continuous-Time Markov Processes -- 1.2.3 Diffusion Processes -- 1.2.4 Processes with Independent Increments -- 1.2.5 Processes with Locally Independent Increments -- 1.2.6 Martingale Characterization of Markov Processes -- 1.3 Semi-Markov Processes -- 1.3.1 Markov Renewal Processes -- 1.3.2 Markov Renewal Equation and Theorem -- 1.3.3 Auxiliary Processes -- 1.3.4 Compensating Operators -- 1.3.5 Martingale Characterization of Markov Renewal Processes -- 1.4 Semimartingales -- 1.5 Counting Markov Renewal Processes -- 1.6 Reducible-Invertible Operators -- 2. Stochastic Systems with Switching -- 2.1 Introduction -- 2.2 Stochastic Integral Functionals -- 2.3 Increment Processes -- 2.4 Stochastic Evolutionary Systems -- 2.5 Markov Additive Processes -- 2.6 Stochastic Additive Functionals -- 2.7 Random Evolutions -- 2.7.1 Continuous Random Evolutions -- 2.7.2 Jump Random Evolutions -- 2.7.3 Semi-Markov Random Evolutions -- 2.8 Extended Compensating Operators -- 2.9 Markov Additive Semimartingales -- 2.9.1 Impulsive Processes -- 2.9.2 Continuous Predictable Characteristics -- 3. Stochastic Systems in the Series Scheme -- 3.1 Introduction -- 3.2 Random Evolutions in the Series Scheme -- 3.2.1 Continuous Random Evolutions -- 3.2.2 Jump Random Evolutions -- 3.3 Average Approximation -- 3.3.1 Stochastic Additive Functionals -- 3.3.2 Increment Processes -- 3.4 Diffusion Approximation -- 3.4.1 Stochastic Integral Functionals -- 3.4.2 Stochastic Additive Functionals -- 3.4.3 Stochastic Evolutionary Systems -- 3.4.4 Increment Processes -- 3.5 Diffusion Approximation with Equilibrium -- 3.5.1 Locally Independent Increment Processes -- 3.5.2 Stochastic Additive Functionals with Equilibrium -- 3.5.3 Stochastic Evolutionary Systems with Semi-Markov Switching -- 4. Stochastic Systems with Split and Merging -- 4.1 Introduction -- 4.2 Phase Merging Scheme -- 4.2.1 Ergodic Merging -- 4.2.2 Merging with Absorption -- 4.2.3 Ergodic Double Merging -- 4.3 Average with Merging -- 4.3.1 Ergodic Average -- 4.3.2 Average with Absorption -- 4.3.3 Ergodic Average with Double Merging -- 4.3.4 Double Average with Absorption -- 4.4 Diffusion Approximation with Split and Merging -- 4.4.1 Ergodic Split and Merging -- 4.4.2 Split and Merging with Absorption -- 4.4.3 Ergodic Split and Double Merging -- 4.4.4 Double Split and Merging -- 4.4.5 Double Split and Double Merging -- 4.5 Integral F'unctionals in Split Phase Space -- 4.5.1 Ergodic Split -- 4.5.2 Double Split and Merging -- 4.5.3 Triple Split and Merging -- 5. Phase Merging Principles -- 5.1 Introduction -- 5.2 Perturbation of Reducible-Invertible Operators -- 5.2.1 Preliminaries -- 5.2.2 Solution of Singular Perturbation Problems -- 5.3 Average Merging Principle -- 5.3.1 Stochastic Evolutionary Systems -- 5.3.2 Stochastic Additive F'unctionals -- 5.3.3 Increment Processes -- 5.3.4 Continuous Random Evolutions -- 5.3.5 Jump Random Evolutions -- 5.3.6 Random Evolutions with Markov Switching -- 5.4 Diffusion Approximation Principle -- 5.4.1 Stochastic Integral F'unctionals -- 5.4.2 Continuous Random Evolutions -- 5.4.3 Jump Random Evolution. Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Processus stochastiques. Optimisation mathématique. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Mathematical optimization fast Stochastic processes fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85128181 http://id.loc.gov/authorities/subjects/sh85082127 https://id.nlm.nih.gov/mesh/D013269 |
| title | Stochastic systems in merging phase space / |
| title_auth | Stochastic systems in merging phase space / |
| title_exact_search | Stochastic systems in merging phase space / |
| title_full | Stochastic systems in merging phase space / Vladimir S. Koroliuk, Nikolas Limnios. |
| title_fullStr | Stochastic systems in merging phase space / Vladimir S. Koroliuk, Nikolas Limnios. |
| title_full_unstemmed | Stochastic systems in merging phase space / Vladimir S. Koroliuk, Nikolas Limnios. |
| title_short | Stochastic systems in merging phase space / |
| title_sort | stochastic systems in merging phase space |
| topic | Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Processus stochastiques. Optimisation mathématique. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Mathematical optimization fast Stochastic processes fast |
| topic_facet | Stochastic processes. Mathematical optimization. Stochastic Processes Processus stochastiques. Optimisation mathématique. MATHEMATICS Probability & Statistics Stochastic Processes. Mathematical optimization Stochastic processes Electronic books. |
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