Exponential stability of stochastic differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Dekker
1994
|
| Series: | Pure and applied mathematics
182 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 307 S. |
| ISBN: | 0824790804 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804124159730515968 |
|---|---|
| adam_text | Contents
Preface v
General Notation xi
1. Semimartingales with Spatial Parameters and Stochastic Integrals
1.1. Introduction 1
1.2. Preliminaries on stochastic processes 2
1.3. C semimartingales with spatial parameters 12
1.4. Stochastic integrals with nonlinear integrators 17
1.5. Generalized Ito s formula and others 20
1.6. Time change formula of stochastic integrals 22
1.7. Inequalities 24
2. Stochastic Differential Equations
2.1. Introduction 33
2.2. One dimensional stochastic differential equations 36
2.3. Special d dimensional stochastic differential equations 55
2.4. General d dimensional stochastic differential equations 58
2.5. LP estimates of solutions 72
2.6. Almost surely asymptotic bounds of solutions 76
2.7. Stochastic flows and stochastic differential equations 89
3. Stochastic Differential Delay Equations
3.1. Introduction 93
3.2. Existence and uniqueness of solutions 94
3.3. Bounded stochastic integral contractors and solutions 101
3.4. Cauchy Maruyama s approximate solutions 117
3.5. Caratheodory s approximate solutions 124
3.6. LP estimates 132
3.7. Almost surely asymptotic bounds of solutions 136
ix
x Contents
4. Exponential Stability of Stochastic Differential Equations
4.1. Introduction 147
4.2. Almost sure exponential stability 148
4.3. Pthmoment exponential stability 163
4.4. Stochastic stabilization and destabilization 167
4.5. Lyapunov exponents of stochastic flows 172
4.6. Stochastic oscillators 176
5. Almost Sure Exponential Stability of Stochastic Differential Delay Equations
5.1. Introduction 183
5.2. Equations with constant delay 184
5.3. Equations with variable delay 195
5.4. Stochastic differential functional equations 201
5.5. Examples 215
6. Moment Exponential Stability of Stochastic Differential Delay Equations
6.1. Introduction 223
6.2. Pth moment exponential stability of delay equations 224
6.3. Generalizations 229
6.4. Pth moment exponential stability of functional equations 238
6.5. Pth moment exponential stability of functional equations with
perturbation 243
6.6. Examples 251
7. Exponential Stability of Stochastic Differential Equations with Small Time Lag
7.1. Introduction 259
7.2. Linear equations with small time lag 260
7.3. Semi linear equations with small time lag 265
7.4. Non linear equations with small time lag 266
7.5. Further remarks and examples 273
8. Exponential Stability of Large Scale Stochastic Differential Delay Systems
8.1. Introduction 277
8.2. Definitions and relationships between various exponential stabilities 279
8.3. Large scale stochastic delay systems in hierarchical form 283
8.4. General large scale stochastic delay systems 288
8.5. Applications 290
References 295
Index 305
|
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| dewey-sort | 3519.2 |
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| id | DE-604.BV009808164 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:41:14Z |
| institution | BVB |
| isbn | 0824790804 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006491142 |
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| physical | XII, 307 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Mao, Xuerong Verfasser aut Exponential stability of stochastic differential equations Xuerong Mao New York u.a. Dekker 1994 XII, 307 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 182 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Stabilität (DE-588)4056693-6 s DE-604 Pure and applied mathematics 182 (DE-604)BV000001885 182 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006491142&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mao, Xuerong Exponential stability of stochastic differential equations Pure and applied mathematics Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stabilität (DE-588)4056693-6 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4056693-6 |
| title | Exponential stability of stochastic differential equations |
| title_auth | Exponential stability of stochastic differential equations |
| title_exact_search | Exponential stability of stochastic differential equations |
| title_full | Exponential stability of stochastic differential equations Xuerong Mao |
| title_fullStr | Exponential stability of stochastic differential equations Xuerong Mao |
| title_full_unstemmed | Exponential stability of stochastic differential equations Xuerong Mao |
| title_short | Exponential stability of stochastic differential equations |
| title_sort | exponential stability of stochastic differential equations |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stabilität (DE-588)4056693-6 gnd |
| topic_facet | Stochastische Differentialgleichung Stabilität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006491142&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT maoxuerong exponentialstabilityofstochasticdifferentialequations |