An introduction to stochastic dynamics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Cambridge University Press
2015
|
| Edition: | 1. publ. |
| Series: | Cambridge texts in applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seiten 273-285 |
| Physical Description: | xvii, 291 Seiten Diagramme |
| ISBN: | 9781107075399 9781107428201 |
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| 245 | 1 | 0 | |a An introduction to stochastic dynamics |c Jinqiao Duan, Illinois Institute of Technology |
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Record in the Search Index
| _version_ | 1804176517870125056 |
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| adam_text | Titel: An introduction to stochastic dynamics
Autor: Duan, Jinqiao
Jahr: 2015
Contents
Preface page xi
Notation xv
1 Introduction 1
1.1 Examples of Deterministic Dynamical Systems 1
1.2 Examples of Stochastic Dynamical Systems 9
1.3 Mathematical Modeling with Stochastic Differential
Equations 11
1.4 Outline of This Book 11
1.5 Problems 13
2 Background in Analysis and Probability 14
2.1 Euclidean Space 14
2.2 Hilbert, Banach, and Metrie Spaces 15
2.3 Taylor Expansions 16
2.4 Improper Integrals and Cauchy Principal Values 17
2.5 Some Useful Inequalities 19
2.6 Holder Spaces, Sobolev Spaces, and Related Inequalities 22
2.7 Probability Spaces 27
2.8 Stochastic Processes 35
2.9 Convergence Concepts 38
2.10 Simulation 39
2.11 Problems 41
3 Noise 44
3.1 Brownian Motion 44
3.2 What Is Gaussian White Noise? 50
3.3 *A Mathematical Model for Gaussian White Noise 52
vii
viii
Contents
3.4 Simulation 56
3.5 Problems 58
4 A Crash Course in Stochastic Differential Equations 61
4.1 Differential Equations with Noise 61
4.2 Riemann-Stieltjes Integration 62
4.3 Stochastic Integration and Stochastic Differential
Equations 63
4.4 Itö s Formula 75
4.5 Linear Stochastic Differential Equations 82
4.6 Nonlinear Stochastic Differential Equations 88
4.7 Conversion between Itö and Stratonovich Stochastic
Differential Equations 89
4.8 Impact of Noise on Dynamics 92
4.9 Simulation 94
4.10 Problems 95
5 Deterministic Quantities for Stochastic Dynamics 99
5.1 Moments 100
5.2 Probability Density Functions 102
5.3 Most Probable Phase Portraits 111
5.4 MeanExitTime 118
5.5 Escape Probability 123
5.6 Problems 129
6 Invariant Structures for Stochastic Dynamics 133
6.1 Deterministic Dynamical Systems 134
6.2 Measurable Dynamical Systems 148
6.3 Random Dynamical Systems 150
6.4 Linear Stochastic Dynamics 160
6.5 *Random Invariant Manifolds 170
6.6 Problems 180
7 Dynamical Systems Driven by Non-Gaussian Levy Motions 188
7.1 Modeling via Stochastic Differential Equations with
Levy Motions 189
7.2 Levy Motions 190
7.3 The a-Stable Levy Motions 197
7.4 Stochastic Differential Equations with Levy Motions 214
7.5 MeanExitTime 221
Contents
ix
7.6 Escape Probability and Transition Phenomena 228
7.7 Fokker-Planck Equations 237
7.8 Problems 241
Hints and Solutions 245
Further Readings 271
References 273
Index 287
|
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| author | Duan, Jinqiao |
| author_GND | (DE-588)122723120 |
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| ctrlnum | (OCoLC)935771749 (DE-599)GBV81239660X |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:27Z |
| institution | BVB |
| isbn | 9781107075399 9781107428201 |
| language | English |
| lccn | 2014046699 |
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| physical | xvii, 291 Seiten Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge texts in applied mathematics |
| spelling | Duan, Jinqiao Verfasser (DE-588)122723120 aut An introduction to stochastic dynamics Jinqiao Duan, Illinois Institute of Technology 1. publ. New York, NY Cambridge University Press 2015 xvii, 291 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge texts in applied mathematics Literaturverzeichnis: Seiten 273-285 Stochastic processes Probabilities Dynamisches System (DE-588)4013396-5 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische dynamische Optimierung (DE-588)4183372-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Stochastische dynamische Optimierung (DE-588)4183372-7 s Dynamisches System (DE-588)4013396-5 s Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 DE-601 application/pdf http://www.gbv.de/dms/tib-ub-hannover/81239660x.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029135908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duan, Jinqiao An introduction to stochastic dynamics Stochastic processes Probabilities Dynamisches System (DE-588)4013396-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastische dynamische Optimierung (DE-588)4183372-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4057621-8 (DE-588)4183372-7 (DE-588)4057630-9 |
| title | An introduction to stochastic dynamics |
| title_auth | An introduction to stochastic dynamics |
| title_exact_search | An introduction to stochastic dynamics |
| title_full | An introduction to stochastic dynamics Jinqiao Duan, Illinois Institute of Technology |
| title_fullStr | An introduction to stochastic dynamics Jinqiao Duan, Illinois Institute of Technology |
| title_full_unstemmed | An introduction to stochastic dynamics Jinqiao Duan, Illinois Institute of Technology |
| title_short | An introduction to stochastic dynamics |
| title_sort | an introduction to stochastic dynamics |
| topic | Stochastic processes Probabilities Dynamisches System (DE-588)4013396-5 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastische dynamische Optimierung (DE-588)4183372-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Probabilities Dynamisches System Stochastische Differentialgleichung Stochastische dynamische Optimierung Stochastischer Prozess |
| url | http://www.gbv.de/dms/tib-ub-hannover/81239660x.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029135908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT duanjinqiao anintroductiontostochasticdynamics |
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