Introduction to stochastic differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
New York u.a.
Dekker
1988
|
| Edition: | 1. print. |
| Series: | Pure and applied mathematics
114. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 234 S. |
| ISBN: | 082477776X |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to stochastic differential equations |
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Record in the Search Index
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| adam_text | Contents
Preface v
1. PROBABILITY AND STOCHASTIC PROCESSES 1
1.0 Introduction 1
1.1 Probability Spaces, Random Variables, and Distributions 2
1.2 Expectation 6
1.3 Independence, Conditional Expectation, and Conditional
Probability 9
1.4 Limit Theorems 14
1.5 Basic Properties of Stochastic Processes 19
1.6 Stationary Processes with Independent Increments 23
1.7 Markov Processes 25
1.8 Diffusion Processes 29
1.9 Wiener Process and White Noise 31
2. STOCHASTIC INTEGRALS AND ITO S FORMULA 35
2.0 Introduction 35
2.1 Nonanticipating Functions 37
2.2 Definition of the Ito Stochastic Integral 43
2.3 Stochastic Integrals as Functions of the Upper Limit 48
2.4 Ito s Formula 53
Exercises 62
ix
x Contents
3. BASIC THEORY OF STOCHASTIC DIFFERENTIAL
EQUATIONS 64
3.0 Ordinary, Random, and Stochastic Differential Equations:
Fundamental Questions and Properties 64
3.1 Existence and Uniqueness of Solutions; Dependence on
Parameters and Initial Conditions 68
3.2 Ito s Formula and Moments of Solutions of Stochastic
Differential Equations 81
3.3 Solutions of Stochastic Differential Equations as Diffusion
Processes 85
3.4 Stratonovich s Stochastic Integral 95
3.5 Solutions of Some Partial Differential Equations: Exit
Probabilities 103
Exercises 107
4. SOLVING STOCHASTIC DIFFERENTIAL EQUATIONS 109
4.0 Introduction: Reducing Stochastic Differential Equations 109
4.1 Scalar Differential Equations 110
4.2 Linear Stochastic Differential Equations 117
4.3 Simulation by a Decoupled System 122
Exercises 125
5. QUALITATIVE THEORY OF STOCHASTIC DIFFEREN¬
TIAL EQUATIONS 126
5.0 Introduction 126
5.1 Boundedness of Solutions 127
5.2 Stability 133
5.3 Further Remarks on Stochastic Stability 140
5.4 Qualitative Theory of Scalar Diffusion Processes:
Boundary Classification 145
5.5 A Uniqueness Result 151
Exercises 154
6. APPLICATIONS IN BIOLOGY: POPULATION DYNAMICS 157
6.0 Introduction 157
6.1 Modeling Considerations and Approximations 158
6.2 Some Population Dynamics Models 168
6.3 Multispecies Population Dynamics 173
6.3.1 Deterministic Models 173
Contents xi
6.3.2 Stochastic Multispecies Models: Nondegenerate
Case 175
6.3.3 Degenerate Noise Intensity: A Special Case 179
Exercises 181
7. QUANTITATIVE THEORY OF STOCHASTIC DIFFEREN¬
TIAL EQUATIONS: SAMPLE PATH APPROXIMATIONS 183
7.0 Introduction 183
7.1 Euler s Method 186
7.2 Heun s Method 192
7.3 Higher Order Runge Kutta Type Schemes 200
7.4 Systems of Stochastic Equations 208
7.5 Remarks on Methods Generated by Iterated Stochastic
Integrals 211
Exercises 217
References 219
Author Index 227
Subject Index 229
I
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| any_adam_object | 1 |
| author | Gard, Thomas C. |
| author_facet | Gard, Thomas C. |
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| author_sort | Gard, Thomas C. |
| author_variant | t c g tc tcg |
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| bvnumber | BV003515371 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)246624878 (DE-599)BVBBV003515371 |
| discipline | Mathematik |
| edition | 1. print. |
| format | Book |
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| id | DE-604.BV003515371 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:01:08Z |
| institution | BVB |
| isbn | 082477776X |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002229956 |
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| physical | XI, 234 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Gard, Thomas C. Verfasser aut Introduction to stochastic differential equations 1. print. New York u.a. Dekker 1988 XI, 234 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 114. Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Pure and applied mathematics 114. (DE-604)BV000001885 114. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002229956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gard, Thomas C. Introduction to stochastic differential equations Pure and applied mathematics Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4057621-8 |
| title | Introduction to stochastic differential equations |
| title_auth | Introduction to stochastic differential equations |
| title_exact_search | Introduction to stochastic differential equations |
| title_full | Introduction to stochastic differential equations |
| title_fullStr | Introduction to stochastic differential equations |
| title_full_unstemmed | Introduction to stochastic differential equations |
| title_short | Introduction to stochastic differential equations |
| title_sort | introduction to stochastic differential equations |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002229956&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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