Introduction to stochastic processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2021]
|
| Series: | World Scientific series on probability theory and its applications
Volume 2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 230 Seiten Diagramme |
| ISBN: | 9789814740302 |
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Record in the Search Index
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| adam_text | Contents Preface to the English Edition v Preface to the Chinese Edition vii Markov Processes 1 1. 3 Discrete-Time Markov Chains 1.1 1.2 1.3 1.4 1.5 1.6 2. 3. Stochastic Models for Economic Optimization and Markov Chains.................................................................... Discrete-Time Markov Chains. Recurrence and Ergodicity Limit Theorems in General Situation................................ Criteria. The Minimal Nonnegative Solution..................... Some Typical Discrete-Time Markov Chains..................... Supplements and Exercises.................................................. 3 11 24 30 39 44 Continuous-Time Markov Chains 55 2.1 2.2 2.3 2.4 2.5 55 63 70 78 82 Continuous-Time Markov Chains. Uniqueness.................. Recurrence and Ergodicity.................................................. Single Birth Processes and Birth-Death Processes............ Branching Processes and Extended Branching Processes . Supplements and Exercises.................................................. Reversible Markov Chains 89 3.1 3.2 89 91 Reversible and Symmetrizable Markov Chains.................. Estimate of Spectral Gap .................................................. xi
CONTENTS Xli 3.3 3.4 4. Appendix: Spectral Representation of Reversible Markov Chains...................................................................................... Supplements and Exercises..................................................... General Markov Processes 109 4.1 4.2 4.3 109 114 4.4 Markov Property and Its Equivalence ................................... Strong Markov Property........................................................ Appendix: Optimal Stopping Problem—The Secretary Problem................................................................................... Supplements and Exercises.................................................... Stochastic Analysis 5. Martingale 5.1 5.2 5.3 5.4 5.5 5.6 5.7 6. 7. 105 119 121 123 125 Definitions and Basic Properties........................................... 125 Doob’s Stopping Theorem..................................................... 127 Fundamental Inequalities....................................................... 129 Convergence Theorems........................................................... 133 Continuous-Time (Sub/Super)Martingale ......................... 139 Two Applications of Martingale Theory............................ 140 Supplements and Exercises..................................................... 144 Brownian Motion 147 6.1 6.2 6.3 6.4 6.5 147 149 152 154 154 Brownian Motion.................................................................... The Trajectory Property........................................................ Martingale Property of Brownian Motion .........................
Multi-Dimensional Brownian Motion.................................. Supplements and Exercises..................................................... Stochastic Integral and Diffusion Processes 7.1 7.2 7.3 7.4 7.5 159 Stochastic Integral................................................................. 159 Itô’s Formula.......................................................................... 163 Stochastic Differential Equation (SDE) (Dimension One) . 165 One-Dimensional Diffusion Process..................................... 168 Supplements and Exercises..................................................... 174
8. CONTENTS xiii Semimartingale and Stochastic Integral 179 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 179 182 185 186 189 193 195 197 Uniqueness of Doob-Meyer Decomposition......................... Existence of Doob-Meyer Decomposition............................ Properties of Variation Processes........................................ Stochastic Integral................................................................. Itô’s Formula.......................................................................... Local Martingale and Semimartingale ............................... Multivariate Stochastic Integral........................................... Stochastic Differential Equation (Multidimension)............ Feynman-Kac Formula, Random Change of Time, and Girsanov’s Theorem .............................................................. 8.10 Supplements and Exercises.................................................... 201 213 Notes 219 Bibliography 223 Index 227
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| any_adam_object | 1 |
| author | Chen, Mufa 1947- Mao, Yong-Hua ca. 20./21. Jh |
| author_GND | (DE-588)129732095 (DE-588)1247132315 |
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| author_sort | Chen, Mufa 1947- |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:14:15Z |
| institution | BVB |
| isbn | 9789814740302 |
| language | English |
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| physical | xiii, 230 Seiten Diagramme |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | World Scientific |
| record_format | marc |
| series | World Scientific series on probability theory and its applications |
| series2 | World Scientific series on probability theory and its applications |
| spelling | Chen, Mufa 1947- (DE-588)129732095 aut Introduction to stochastic processes Mu-Fa Chen ; Yong-Hua Mao ; Beijing Normal University, China New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2021] © 2021 xiii, 230 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier World Scientific series on probability theory and its applications Volume 2 Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Stochastische Analysis (DE-588)4132272-1 s DE-604 Mao, Yong-Hua ca. 20./21. Jh. (DE-588)1247132315 aut Erscheint auch als Online-Ausgabe 978-981-4740-31-9 World Scientific series on probability theory and its applications Volume 2 (DE-604)BV042764310 2 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030687745&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, Mufa 1947- Mao, Yong-Hua ca. 20./21. Jh Introduction to stochastic processes World Scientific series on probability theory and its applications Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4132272-1 |
| title | Introduction to stochastic processes |
| title_auth | Introduction to stochastic processes |
| title_exact_search | Introduction to stochastic processes |
| title_full | Introduction to stochastic processes Mu-Fa Chen ; Yong-Hua Mao ; Beijing Normal University, China |
| title_fullStr | Introduction to stochastic processes Mu-Fa Chen ; Yong-Hua Mao ; Beijing Normal University, China |
| title_full_unstemmed | Introduction to stochastic processes Mu-Fa Chen ; Yong-Hua Mao ; Beijing Normal University, China |
| title_short | Introduction to stochastic processes |
| title_sort | introduction to stochastic processes |
| topic | Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Analysis (DE-588)4132272-1 gnd |
| topic_facet | Stochastischer Prozess Stochastische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030687745&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042764310 |
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