Stability of stochastic differential equations with respect to semimartingales:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Longman Scientific & Technical
1991
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
251 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 276 S. |
| ISBN: | 0582080363 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stability of stochastic differential equations with respect to semimartingales |c X. Mao |
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Record in the Search Index
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| adam_text | Contents
Preface
1 Stochastic Differential Equations 1
1.1 Introduction 1
1.2 Semimartingales and stochastic integrals 1
1.3 Stochastic differential equations 9
1.4 Generalized theorems of existence and uniqueness 25
1.5 Applications to Doleans Dade s equations 30
1.6 Applications to delay SDES 33
1.7 Delay Doleans Dade s equations 44
2 Inequalities 47
2.1 Introduction 47
2.2 Notations 47
2.3 Lebesgue Stieltjes integral inequalities 49
2.4 Inequalities with retardation 56
2.5 Discrete inequalities 63
2.6 Stochastic integral inequalities 67
2.7 Further integral inequalities 72
3 Stochastic Stability Theory 76
3.1 Introduction 76
3.2 Stability in probability 76
3.3 Lyapunov functions and Lyapunov exponents 85
3.4 Moment exponential stability 102
3.5 Bound for Lyapunov exponents of stochastic flows 105
4 Stability of Stochastic Perturbed Systems 109
4.1 Introduction 109
4.2 Almost sure exponential stability of semilinear perturbed systems 110
4.3 Almost sure exponential stability of nonlinear perturbed systems 121
4.4 Generalizations 132
4.5 Moment exponential stability of perturbed systems 145
4.6 Eventual stability of stochastic perturbed systems 155
5 Stability of Stochastic Delay Equations 165
5.1 Introduction 165
5.2 Stability in probability of stochastic delay equations 165
5.3 Moment exponential stability of delay equations 177
5.4 Almost sure exponential stability of delay equations 186
6 Polynomial Stability of Stochastic Differential Equations 197
6.1 Introduction 197
6.2 Lyapunov functions and polynomial stability 198
6.3 Polynomial stability of perturbed stochastic systems 206
6.4 Polynomial stability of stochastic delay equations 220
7 Comparison Theorems and Stability 232
7.1 Introduction 232
7.2 Comparison theorems between a stochastic differential equation
and an ordinary differential equation 233
7.3 Comparison theorems between two SDES 237
7.4 Examples 242
8 A Transformation Formula and Stability 248
8.1 Introduction 248
8.2 Transformation formula for stochastic integrals 248
8.3 Applications to stochastic stability 253
8.4 Stability of stochastic differential delay equations 258
References 267
Index 275
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| author_facet | Mao, Xuerong |
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| author_sort | Mao, Xuerong |
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| discipline | Mathematik |
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| id | DE-604.BV004463982 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:13:23Z |
| institution | BVB |
| isbn | 0582080363 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002767206 |
| oclc_num | 439808766 |
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| physical | 276 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Mao, Xuerong Verfasser aut Stability of stochastic differential equations with respect to semimartingales X. Mao 1. publ. New York Longman Scientific & Technical 1991 276 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 251 Verjetnost - Stohastične diferencialne enačbe Stabilität (DE-588)4056693-6 gnd rswk-swf Semimartingal (DE-588)4180967-1 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Fixpunkttheorie (DE-588)4293945-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Stabilität (DE-588)4056693-6 s Semimartingal (DE-588)4180967-1 s DE-604 Fixpunkttheorie (DE-588)4293945-8 s Pitman research notes in mathematics series 251 (DE-604)BV000022845 251 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002767206&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mao, Xuerong Stability of stochastic differential equations with respect to semimartingales Pitman research notes in mathematics series Verjetnost - Stohastične diferencialne enačbe Stabilität (DE-588)4056693-6 gnd Semimartingal (DE-588)4180967-1 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Fixpunkttheorie (DE-588)4293945-8 gnd |
| subject_GND | (DE-588)4056693-6 (DE-588)4180967-1 (DE-588)4057621-8 (DE-588)4293945-8 |
| title | Stability of stochastic differential equations with respect to semimartingales |
| title_auth | Stability of stochastic differential equations with respect to semimartingales |
| title_exact_search | Stability of stochastic differential equations with respect to semimartingales |
| title_full | Stability of stochastic differential equations with respect to semimartingales X. Mao |
| title_fullStr | Stability of stochastic differential equations with respect to semimartingales X. Mao |
| title_full_unstemmed | Stability of stochastic differential equations with respect to semimartingales X. Mao |
| title_short | Stability of stochastic differential equations with respect to semimartingales |
| title_sort | stability of stochastic differential equations with respect to semimartingales |
| topic | Verjetnost - Stohastične diferencialne enačbe Stabilität (DE-588)4056693-6 gnd Semimartingal (DE-588)4180967-1 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Fixpunkttheorie (DE-588)4293945-8 gnd |
| topic_facet | Verjetnost - Stohastične diferencialne enačbe Stabilität Semimartingal Stochastische Differentialgleichung Fixpunkttheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002767206&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022845 |
| work_keys_str_mv | AT maoxuerong stabilityofstochasticdifferentialequationswithrespecttosemimartingales |