Continuous-time Markov chains and applications: a singular perturbation approach
This book discusses continuous-time Markov chains and applications. Using a singular perturbation approach, it presents a systematic treatment of singularly perturbed systems that naturally arise in queueing theory, control and optimization, and manufacturing systems. It gathers a number of ideas in...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
1998
|
| Schriftenreihe: | Applications of mathematics
37 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book discusses continuous-time Markov chains and applications. Using a singular perturbation approach, it presents a systematic treatment of singularly perturbed systems that naturally arise in queueing theory, control and optimization, and manufacturing systems. It gathers a number of ideas in Markov chains and singular perturbations that are scattered throughout the literature. It presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. The emphasis is on Markov chains with weak and strong interactions and structural properties. Much of the content is an outgrowth of the authors' recent research. Some of the results have not appeared elsewhere. This book will be an important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimization. |
| Beschreibung: | XV, 349 S. |
| ISBN: | 0387982442 9780387982441 |
Internformat
MARC
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| 245 | 1 | 0 | |a Continuous-time Markov chains and applications |b a singular perturbation approach |c G. George Yin ; Qing Zhang |
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| 300 | |a XV, 349 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Applications of mathematics |v 37 | |
| 520 | 3 | |a This book discusses continuous-time Markov chains and applications. Using a singular perturbation approach, it presents a systematic treatment of singularly perturbed systems that naturally arise in queueing theory, control and optimization, and manufacturing systems. It gathers a number of ideas in Markov chains and singular perturbations that are scattered throughout the literature. It presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. The emphasis is on Markov chains with weak and strong interactions and structural properties. Much of the content is an outgrowth of the authors' recent research. Some of the results have not appeared elsewhere. This book will be an important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimization. | |
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| 700 | 1 | |a Zhang, Qing |e Sonstige |4 oth | |
| 830 | 0 | |a Applications of mathematics |v 37 |w (DE-604)BV000895226 |9 37 | |
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Datensatz im Suchindex
| _version_ | 1804126320814194688 |
|---|---|
| adam_text | Contents
Preface xi
Notation xiii
I Prologue and Preliminaries 1
1 Introduction and Overview 3
1.1 Introduction 3
1.2 A Brief Survey 8
1.3 Outline of the Book 10
2 Mathematical Preliminaries 15
2.1 Introduction 15
2.2 Martingales 15
2.3 Markov Chains 16
2.4 Piecewise Deterministic Processes 19
2.5 Irreducibility and Quasi Stationary Distributions 21
2.6 Gaussian Processes and Diffusions 23
2.7 Notes 24
3 Markovian Models 25
3.1 Introduction 25
3.2 Birth and Death Processes 26
3.3 Finite State Space Models 28
x Contents
3.4 Stochastic Optimization Problems 39
3.5 Linear Systems with Jump Markov Disturbance 43
3.6 Interpretations of Time Scale Separation 47
3.7 Notes 49
II Singularly Perturbed Markov Chains 51
4 Asymptotic Expansion: Irreducible Generators 53
4.1 Introduction 53
4.2 Asymptotic Expansion 55
4.3 Regular Part of the Expansion 58
4.4 Boundary Layer Correction 62
4.5 Asymptotic Validation 66
4.6 Examples 70
4.7 Two Time Scale Expansion 73
4.8 Notes 77
5 Asymptotic Normality and Exponential Bounds 79
5.1 Introduction 79
5.2 Occupation Measure 81
5.3 Exponential Bounds 86
5.4 Asymptotic Normality 95
5.5 Extensions 105
5.6 Notes 108
6 Asymptotic Expansion: Weak and Strong Interactions 111
6.1 Introduction Ill
6.2 Chains with Recurrent States 114
6.3 Inclusion of Absorbing States 134
6.4 Inclusion of Transient States 142
6.5 Countable State Space Part I 154
6.6 Countable State Space Part II 156
6.7 Remarks on Singularly Perturbed Diffusions 161
6.8 Notes 165
7 Weak and Strong Interactions: Asymptotic Properties and
Ramification 167
7.1 Introduction 167
7.2 Aggregation of Markov Chains 169
7.3 Exponential Bounds 176
7.4 Asymptotic Normality 185
7.5 Measurable Generators 207
7.6 Notes 216
Contents xi
III Control and Numerical Methods 219
8 Markov Decision Problems 221
8.1 Introduction 221
8.2 Problem Formulation 223
8.3 Limit Problem 225
8.4 Asymptotic Optimality 229
8.5 Convergence Rate and Error Bound 232
8.6 Long Run Average Cost 234
8.7 Computational Procedures 240
8.8 Notes 242
9 Stochastic Control of Dynamical Systems 243
9.1 Introduction 243
9.2 Problem Formulation 245
9.3 Properties of the Value Functions 247
9.4 Asymptotic Optimal Controls 254
9.5 Convergence Rate 258
9.6 Weak Convergence Approach 264
9.7 Notes 274
10 Numerical Methods for Control and Optimization 277
10.1 Introduction 277
10.2 Numerical Methods for Optimal Control 279
10.3 Optimization under Threshold Policy 282
10.4 Notes 298
A Appendix 299
A.I Properties of Generators 299
A.2 Weak Convergence 302
A.3 Relaxed Control 308
A.4 Viscosity Solutions of HJB Equations 309
A.5 Value Functions and Optimal Controls 314
A.6 Miscellany 325
References 333
Index 347
|
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| id | DE-604.BV011777710 |
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| indexdate | 2024-07-09T18:15:35Z |
| institution | BVB |
| isbn | 0387982442 9780387982441 |
| language | English |
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| spelling | Yin, George 1954- Verfasser (DE-588)115596798 aut Continuous-time Markov chains and applications a singular perturbation approach G. George Yin ; Qing Zhang New York Springer 1998 XV, 349 S. txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 37 This book discusses continuous-time Markov chains and applications. Using a singular perturbation approach, it presents a systematic treatment of singularly perturbed systems that naturally arise in queueing theory, control and optimization, and manufacturing systems. It gathers a number of ideas in Markov chains and singular perturbations that are scattered throughout the literature. It presents results on asymptotic expansions of the corresponding probability distributions, functional occupation measures, exponential upper bounds, and asymptotic normality. The emphasis is on Markov chains with weak and strong interactions and structural properties. Much of the content is an outgrowth of the authors' recent research. Some of the results have not appeared elsewhere. This book will be an important reference for researchers in applied mathematics, probability and stochastic processes, operations research, control theory, and optimization. Controleleer gtt Markov-processen gtt Markov processes Perturbation (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd rswk-swf Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd rswk-swf Markov-Kette mit stetiger Zeit (DE-588)4272650-5 s Singuläre Störung (DE-588)4055100-3 s DE-604 Zhang, Qing Sonstige oth Applications of mathematics 37 (DE-604)BV000895226 37 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007948532&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yin, George 1954- Continuous-time Markov chains and applications a singular perturbation approach Applications of mathematics Controleleer gtt Markov-processen gtt Markov processes Perturbation (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd |
| subject_GND | (DE-588)4055100-3 (DE-588)4272650-5 |
| title | Continuous-time Markov chains and applications a singular perturbation approach |
| title_auth | Continuous-time Markov chains and applications a singular perturbation approach |
| title_exact_search | Continuous-time Markov chains and applications a singular perturbation approach |
| title_full | Continuous-time Markov chains and applications a singular perturbation approach G. George Yin ; Qing Zhang |
| title_fullStr | Continuous-time Markov chains and applications a singular perturbation approach G. George Yin ; Qing Zhang |
| title_full_unstemmed | Continuous-time Markov chains and applications a singular perturbation approach G. George Yin ; Qing Zhang |
| title_short | Continuous-time Markov chains and applications |
| title_sort | continuous time markov chains and applications a singular perturbation approach |
| title_sub | a singular perturbation approach |
| topic | Controleleer gtt Markov-processen gtt Markov processes Perturbation (Mathematics) Singuläre Störung (DE-588)4055100-3 gnd Markov-Kette mit stetiger Zeit (DE-588)4272650-5 gnd |
| topic_facet | Controleleer Markov-processen Markov processes Perturbation (Mathematics) Singuläre Störung Markov-Kette mit stetiger Zeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007948532&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
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