Stochastic differential equations with Markovian switching:
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| Main Authors: | , |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
London
Imperial College Press
[2006]
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| Subjects: | |
| Online Access: | TUM01 TUM02 UBM01 Volltext |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 1860947018 1860948847 9781860948848 9781860947018 |
| DOI: | 10.1142/p473 |
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| 505 | 8 | |a Intro; Contents; Preface; Notation; 1. Brownian Motions and Stochastic Integrals; 1.1 Introduction; 1.2 Basic Notations of Probability Theory; 1.3 Stochastic Processes; 1.4 Brownian Motions; 1.5 Stochastic Integrals; 1.6 Ito's Formula; 1.7 Markov Processes; 1.8 Generalised Ito's Formula; 1.9 Exercises; 2. Inequalities; 2.1 Introduction; 2.2 Frequently Used Inequalities; 2.3 Gronwall-Type Inequalities; 2.4 Matrices and Inequalities; 2.5 Linear Matrix Inequalities; 2.6 M-Matrix Inequalities; 2.7 Stochastic Inequalities; 2.8 Exercises | |
| 505 | 8 | |a 3. Stochastic Differential Equations with Markovian Switching3.1 Introduction; 3.2 Stochastic Differential Equations; 3.3 Existence and Uniqueness of Solutions; 3.4 SDEs with Markovian Switching; 3.5 Lp-Estimates; 3.6 Almost Surely Asymptotic Estimates; 3.7 Solutions as Markov Processes; 3.8 Exercises; 4. Approximate Solutions; 4.1 Introduction; 4.2 Euler-Maruyama's Approximations; 4.2.1 Global Lipschitz Case; 4.2.2 Local Lipschitz Case; 4.2.3 More on Local Lipschitz Case; 4.3 Caratheodory's Approximations; 4.4 Split-Step Backward Euler Scheme; 4.5 Backward Euler Scheme | |
| 505 | 8 | |a 4.6 Stochastic Theta Method4.7 Exercises; 5. Boundedness and Stability; 5.1 Introduction; 5.2 Asymptotic Boundedness; 5.3 Exponential Stability; 5.3.1 Nonlinear Jump Systems; 5.3.2 Multi-Dimensional Linear Equations; 5.3.3 Scalar Linear Equations; 5.3.4 Examples; 5.4 Moment and Almost Sure Asymptotic Stability; 5.5 Stability in Probability; 5.6 Asymptotic Stability in Distribution; 5.7 Exercises; 6. Numerical Methods for Asymptotic Properties; 6.1 Introduction; 6.2 Euler-Maruyama's Method and Exponential Stability; 6.3 Euler-Maruyama's Method and Lyapunov Exponents | |
| 505 | 8 | |a 6.4 Generalised Results and Stochastic Theta Method6.5 Asymptotic Stability in Distribution of the EM Method: Constant Step Size; 6.5.1 Stability in Distribution of the EM Method; 6.5.2 Sufficient Criteria for Assumptions 6.16-6.18; 6.5.3 Convergence of Stationary Distributions; 6.6 Asymptotic Stability in Distribution of the EM Method: Variable Step Sizes; 6.7 Exercises; 7. Stochastic Differential Delay Equations with Markovian Switching; 7.1 Introduction; 7.2 Stochastic Differential Delay Equations; 7.3 SDDEs with Markovian Switching; 7.4 Moment Properties; 7.5 Asymptotic Boundedness | |
| 505 | 8 | |a 7.6 Exponential Stability7.7 Approximate Solutions; 7.8 Exercises; 8. Stochastic Functional Differential Equations with Markovian Switching; 8.1 Introduction; 8.2 Stochastic Functional Differential Equations; 8.3 SFDEs with Markovian Switching; 8.4 Boundedness; 8.5 Asymptotic Stability; 8.6 Razumikhin-Type Theorems on Stability; 8.7 Examples; 8.8 Exercises; 9. Stochastic Interval Systems with Markovian Switching; 9.1 Introduction; 9.2 Interval Matrices; 9.3 SDISs with Markovian Switching; 9.4 Razumikhin Technology on SDISs; 9.4.1 Delay Independent Criteria; 9.4.2 Delay Dependent Criteria | |
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| author | Mao, Xuerong 1957- Yuan, Chenggui |
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| author_facet | Mao, Xuerong 1957- Yuan, Chenggui |
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| contents | Intro; Contents; Preface; Notation; 1. Brownian Motions and Stochastic Integrals; 1.1 Introduction; 1.2 Basic Notations of Probability Theory; 1.3 Stochastic Processes; 1.4 Brownian Motions; 1.5 Stochastic Integrals; 1.6 Ito's Formula; 1.7 Markov Processes; 1.8 Generalised Ito's Formula; 1.9 Exercises; 2. Inequalities; 2.1 Introduction; 2.2 Frequently Used Inequalities; 2.3 Gronwall-Type Inequalities; 2.4 Matrices and Inequalities; 2.5 Linear Matrix Inequalities; 2.6 M-Matrix Inequalities; 2.7 Stochastic Inequalities; 2.8 Exercises 3. Stochastic Differential Equations with Markovian Switching3.1 Introduction; 3.2 Stochastic Differential Equations; 3.3 Existence and Uniqueness of Solutions; 3.4 SDEs with Markovian Switching; 3.5 Lp-Estimates; 3.6 Almost Surely Asymptotic Estimates; 3.7 Solutions as Markov Processes; 3.8 Exercises; 4. Approximate Solutions; 4.1 Introduction; 4.2 Euler-Maruyama's Approximations; 4.2.1 Global Lipschitz Case; 4.2.2 Local Lipschitz Case; 4.2.3 More on Local Lipschitz Case; 4.3 Caratheodory's Approximations; 4.4 Split-Step Backward Euler Scheme; 4.5 Backward Euler Scheme 4.6 Stochastic Theta Method4.7 Exercises; 5. Boundedness and Stability; 5.1 Introduction; 5.2 Asymptotic Boundedness; 5.3 Exponential Stability; 5.3.1 Nonlinear Jump Systems; 5.3.2 Multi-Dimensional Linear Equations; 5.3.3 Scalar Linear Equations; 5.3.4 Examples; 5.4 Moment and Almost Sure Asymptotic Stability; 5.5 Stability in Probability; 5.6 Asymptotic Stability in Distribution; 5.7 Exercises; 6. Numerical Methods for Asymptotic Properties; 6.1 Introduction; 6.2 Euler-Maruyama's Method and Exponential Stability; 6.3 Euler-Maruyama's Method and Lyapunov Exponents 6.4 Generalised Results and Stochastic Theta Method6.5 Asymptotic Stability in Distribution of the EM Method: Constant Step Size; 6.5.1 Stability in Distribution of the EM Method; 6.5.2 Sufficient Criteria for Assumptions 6.16-6.18; 6.5.3 Convergence of Stationary Distributions; 6.6 Asymptotic Stability in Distribution of the EM Method: Variable Step Sizes; 6.7 Exercises; 7. Stochastic Differential Delay Equations with Markovian Switching; 7.1 Introduction; 7.2 Stochastic Differential Delay Equations; 7.3 SDDEs with Markovian Switching; 7.4 Moment Properties; 7.5 Asymptotic Boundedness 7.6 Exponential Stability7.7 Approximate Solutions; 7.8 Exercises; 8. Stochastic Functional Differential Equations with Markovian Switching; 8.1 Introduction; 8.2 Stochastic Functional Differential Equations; 8.3 SFDEs with Markovian Switching; 8.4 Boundedness; 8.5 Asymptotic Stability; 8.6 Razumikhin-Type Theorems on Stability; 8.7 Examples; 8.8 Exercises; 9. Stochastic Interval Systems with Markovian Switching; 9.1 Introduction; 9.2 Interval Matrices; 9.3 SDISs with Markovian Switching; 9.4 Razumikhin Technology on SDISs; 9.4.1 Delay Independent Criteria; 9.4.2 Delay Dependent Criteria |
| ctrlnum | (OCoLC)1220908671 (DE-599)BVBBV046942483 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1142/p473 |
| format | Electronic eBook |
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| index_date | 2024-07-03T15:38:35Z |
| indexdate | 2024-07-10T08:58:08Z |
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| spelling | Mao, Xuerong 1957- Verfasser (DE-588)1145722040 aut Stochastic differential equations with Markovian switching Xuerong Mao, Chenggui Yuan London Imperial College Press [2006] 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Intro; Contents; Preface; Notation; 1. Brownian Motions and Stochastic Integrals; 1.1 Introduction; 1.2 Basic Notations of Probability Theory; 1.3 Stochastic Processes; 1.4 Brownian Motions; 1.5 Stochastic Integrals; 1.6 Ito's Formula; 1.7 Markov Processes; 1.8 Generalised Ito's Formula; 1.9 Exercises; 2. Inequalities; 2.1 Introduction; 2.2 Frequently Used Inequalities; 2.3 Gronwall-Type Inequalities; 2.4 Matrices and Inequalities; 2.5 Linear Matrix Inequalities; 2.6 M-Matrix Inequalities; 2.7 Stochastic Inequalities; 2.8 Exercises 3. Stochastic Differential Equations with Markovian Switching3.1 Introduction; 3.2 Stochastic Differential Equations; 3.3 Existence and Uniqueness of Solutions; 3.4 SDEs with Markovian Switching; 3.5 Lp-Estimates; 3.6 Almost Surely Asymptotic Estimates; 3.7 Solutions as Markov Processes; 3.8 Exercises; 4. Approximate Solutions; 4.1 Introduction; 4.2 Euler-Maruyama's Approximations; 4.2.1 Global Lipschitz Case; 4.2.2 Local Lipschitz Case; 4.2.3 More on Local Lipschitz Case; 4.3 Caratheodory's Approximations; 4.4 Split-Step Backward Euler Scheme; 4.5 Backward Euler Scheme 4.6 Stochastic Theta Method4.7 Exercises; 5. Boundedness and Stability; 5.1 Introduction; 5.2 Asymptotic Boundedness; 5.3 Exponential Stability; 5.3.1 Nonlinear Jump Systems; 5.3.2 Multi-Dimensional Linear Equations; 5.3.3 Scalar Linear Equations; 5.3.4 Examples; 5.4 Moment and Almost Sure Asymptotic Stability; 5.5 Stability in Probability; 5.6 Asymptotic Stability in Distribution; 5.7 Exercises; 6. Numerical Methods for Asymptotic Properties; 6.1 Introduction; 6.2 Euler-Maruyama's Method and Exponential Stability; 6.3 Euler-Maruyama's Method and Lyapunov Exponents 6.4 Generalised Results and Stochastic Theta Method6.5 Asymptotic Stability in Distribution of the EM Method: Constant Step Size; 6.5.1 Stability in Distribution of the EM Method; 6.5.2 Sufficient Criteria for Assumptions 6.16-6.18; 6.5.3 Convergence of Stationary Distributions; 6.6 Asymptotic Stability in Distribution of the EM Method: Variable Step Sizes; 6.7 Exercises; 7. Stochastic Differential Delay Equations with Markovian Switching; 7.1 Introduction; 7.2 Stochastic Differential Delay Equations; 7.3 SDDEs with Markovian Switching; 7.4 Moment Properties; 7.5 Asymptotic Boundedness 7.6 Exponential Stability7.7 Approximate Solutions; 7.8 Exercises; 8. Stochastic Functional Differential Equations with Markovian Switching; 8.1 Introduction; 8.2 Stochastic Functional Differential Equations; 8.3 SFDEs with Markovian Switching; 8.4 Boundedness; 8.5 Asymptotic Stability; 8.6 Razumikhin-Type Theorems on Stability; 8.7 Examples; 8.8 Exercises; 9. Stochastic Interval Systems with Markovian Switching; 9.1 Introduction; 9.2 Interval Matrices; 9.3 SDISs with Markovian Switching; 9.4 Razumikhin Technology on SDISs; 9.4.1 Delay Independent Criteria; 9.4.2 Delay Dependent Criteria Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Electronic books Stochastische Differentialgleichung (DE-588)4057621-8 s Markov-Prozess (DE-588)4134948-9 s DE-604 Yuan, Chenggui Verfasser (DE-588)1041769113 aut Erscheint auch als Mao, Xuerong Stochastic differential equations with Markovian switching London : Imperial College Press, ©2006 Druck-Ausgabe 978-1-86094-701-8 https://doi.org/10.1142/p473 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mao, Xuerong 1957- Yuan, Chenggui Stochastic differential equations with Markovian switching Intro; Contents; Preface; Notation; 1. Brownian Motions and Stochastic Integrals; 1.1 Introduction; 1.2 Basic Notations of Probability Theory; 1.3 Stochastic Processes; 1.4 Brownian Motions; 1.5 Stochastic Integrals; 1.6 Ito's Formula; 1.7 Markov Processes; 1.8 Generalised Ito's Formula; 1.9 Exercises; 2. Inequalities; 2.1 Introduction; 2.2 Frequently Used Inequalities; 2.3 Gronwall-Type Inequalities; 2.4 Matrices and Inequalities; 2.5 Linear Matrix Inequalities; 2.6 M-Matrix Inequalities; 2.7 Stochastic Inequalities; 2.8 Exercises 3. Stochastic Differential Equations with Markovian Switching3.1 Introduction; 3.2 Stochastic Differential Equations; 3.3 Existence and Uniqueness of Solutions; 3.4 SDEs with Markovian Switching; 3.5 Lp-Estimates; 3.6 Almost Surely Asymptotic Estimates; 3.7 Solutions as Markov Processes; 3.8 Exercises; 4. Approximate Solutions; 4.1 Introduction; 4.2 Euler-Maruyama's Approximations; 4.2.1 Global Lipschitz Case; 4.2.2 Local Lipschitz Case; 4.2.3 More on Local Lipschitz Case; 4.3 Caratheodory's Approximations; 4.4 Split-Step Backward Euler Scheme; 4.5 Backward Euler Scheme 4.6 Stochastic Theta Method4.7 Exercises; 5. Boundedness and Stability; 5.1 Introduction; 5.2 Asymptotic Boundedness; 5.3 Exponential Stability; 5.3.1 Nonlinear Jump Systems; 5.3.2 Multi-Dimensional Linear Equations; 5.3.3 Scalar Linear Equations; 5.3.4 Examples; 5.4 Moment and Almost Sure Asymptotic Stability; 5.5 Stability in Probability; 5.6 Asymptotic Stability in Distribution; 5.7 Exercises; 6. Numerical Methods for Asymptotic Properties; 6.1 Introduction; 6.2 Euler-Maruyama's Method and Exponential Stability; 6.3 Euler-Maruyama's Method and Lyapunov Exponents 6.4 Generalised Results and Stochastic Theta Method6.5 Asymptotic Stability in Distribution of the EM Method: Constant Step Size; 6.5.1 Stability in Distribution of the EM Method; 6.5.2 Sufficient Criteria for Assumptions 6.16-6.18; 6.5.3 Convergence of Stationary Distributions; 6.6 Asymptotic Stability in Distribution of the EM Method: Variable Step Sizes; 6.7 Exercises; 7. Stochastic Differential Delay Equations with Markovian Switching; 7.1 Introduction; 7.2 Stochastic Differential Delay Equations; 7.3 SDDEs with Markovian Switching; 7.4 Moment Properties; 7.5 Asymptotic Boundedness 7.6 Exponential Stability7.7 Approximate Solutions; 7.8 Exercises; 8. Stochastic Functional Differential Equations with Markovian Switching; 8.1 Introduction; 8.2 Stochastic Functional Differential Equations; 8.3 SFDEs with Markovian Switching; 8.4 Boundedness; 8.5 Asymptotic Stability; 8.6 Razumikhin-Type Theorems on Stability; 8.7 Examples; 8.8 Exercises; 9. Stochastic Interval Systems with Markovian Switching; 9.1 Introduction; 9.2 Interval Matrices; 9.3 SDISs with Markovian Switching; 9.4 Razumikhin Technology on SDISs; 9.4.1 Delay Independent Criteria; 9.4.2 Delay Dependent Criteria Stochastische Differentialgleichung (DE-588)4057621-8 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4134948-9 |
| title | Stochastic differential equations with Markovian switching |
| title_auth | Stochastic differential equations with Markovian switching |
| title_exact_search | Stochastic differential equations with Markovian switching |
| title_exact_search_txtP | Stochastic differential equations with Markovian switching |
| title_full | Stochastic differential equations with Markovian switching Xuerong Mao, Chenggui Yuan |
| title_fullStr | Stochastic differential equations with Markovian switching Xuerong Mao, Chenggui Yuan |
| title_full_unstemmed | Stochastic differential equations with Markovian switching Xuerong Mao, Chenggui Yuan |
| title_short | Stochastic differential equations with Markovian switching |
| title_sort | stochastic differential equations with markovian switching |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Stochastische Differentialgleichung Markov-Prozess |
| url | https://doi.org/10.1142/p473 |
| work_keys_str_mv | AT maoxuerong stochasticdifferentialequationswithmarkovianswitching AT yuanchenggui stochasticdifferentialequationswithmarkovianswitching |