Asymptotic methods in the theory of stochastic differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathemat. Soc.
1989
|
| Schriftenreihe: | Translations of mathematical monographs
78. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. - EST: Asimptotičeskie metody teorii stochastičeskich differencial'nych uravnenij <engl.> |
| Beschreibung: | XVI, 339 S. |
| ISBN: | 0821845314 |
Internformat
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| 240 | 1 | 0 | |a Asimptotičeskie metody teorii stochastičeskich differencial'nych uravnenij |
| 245 | 1 | 0 | |a Asymptotic methods in the theory of stochastic differential equations |c A. V. Skorokhod |
| 264 | 1 | |a Providence, RI |b American Mathemat. Soc. |c 1989 | |
| 300 | |a XVI, 339 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 78. | |
| 500 | |a Aus d. Russ. übers. - EST: Asimptotičeskie metody teorii stochastičeskich differencial'nych uravnenij <engl.> | ||
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Datensatz im Suchindex
| _version_ | 1804117901358137344 |
|---|---|
| adam_text | Contents
Foreword ix
List of Notation xi
Introduction xiii
CHAPTER I. Ergodic theorems 1
§ 1. General ergodic theorems 1
1.1. Ergodic theorems for semigroups of measure preserving
transformations 1
1.2. Homogeneous Markov processes. Invariant measures
and ergodic theorems 6
1.3. Harris recurrence 15
§2. Densities for transition probabilities and resolvents for
Markov solutions of stochastic differential equations 23
2.1. Nondegenerate diffusion processes 24
2.2. Diffusion processes with degenerate diffusion 27
2.3. Processes with jumps 35
§3. Ergodic theorems for one dimensional stochastic equations 41
3.1. Diffusion processes on the line 42
3.2. Diffusion processes on an interval 53
3.3. Processes with reflection at the boundary 55
§4. Ergodic theorems for solutions of stochastic equations in Rd 57
4.1. Invariant measures for processes on compact spaces 58
4.2. Locally compact spaces 63
4.3. Solutions of stochastic equations in Rd 66
CHAPTER II. Asymptotic behavior of systems of stochastic
equations containing a small parameter 77
§1. Equations with a small right hand side 77
1.1. A general theorem on convergence to a diffusion process 77
V
vi CONTENTS
1.2. Ordinary differential equations with a random
right hand side 80
1.3. A theorem on integral continuity with respect to a
parameter for diffusion processes 97
1.4. Stochastic equations with small diffusion 99
§2. Processes with rapid switching 102
2.1. Processes with a discrete component 103
2.2. An ergodic theorem for jump processes 106
2.3. An estimate for a process with a discrete component 110
2.4. A limit theorem for processes with rapidly varying
discrete component 114
2.5. Dynamical systems with rapid switching 117
§3. Averaging over variables for systems of stochastic differential
equations 134
3.1. A general theorem on averaging 134
3.2. A diffusion process under the influence of a rapid
dynamical system in the presence of feedback 144
3.3. A dynamical system under the influence of a rapid
diffusion process. Neutral case 156
3.4. A dynamical system under the influence of a rapid
diffusion process. Neutral case, large times 163
CHAPTER III. Stability. Linear systems 183
§ 1. Stability of sample paths of homogeneous Markov processes 183
1.1. Definition 183
1.2. A Feller process on a compact metric space 187
1.3. Stability and instability of one dimensional continuous
processes 196
1.4. Stability and instability of Feller processes in a locally
compact space 198
§2. Linear equations in Rd and the stochastic semigroups
connected with them. Stability 205
2.1. Linear equations 205
2.2. Operator equations. Representation of solutions 211
2.3. Commutative case 222
2.4. Homogeneous case. Invariant subspaces 225
2.5. Mean square stability 231
2.6. Stability with probability 1 236
2.7. ^ Stability 246
CONTENTS vii
§3. Stability of solutions of stochastic differential equations 251
3.1. Stability and instability in first approximation 251
3.2. Diffusion equations with homogeneous coefficients 259
CHAPTER IV. Linear stochastic equations in Hilbert space.
Stochastic semigroups. Stability 271
§ 1. Linear equations with bounded coefficients 271
1.1. General equations in Hilbert space 271
1.2. Linear equations 279
1.3. Linear stochastic equations in Hilbert space 285
1.4. Stochastic Hilbert Schmidt semigroups 291
§2. Strong stochastic semigroups with second moments 296
2.1. Strong and weak random operators 296
2.2. Processes with independent increments that are
continuous in || • ||5 300
2.3. A stochastic differential equation 305
2.4. Second order stochastic semigroups of bounded
variation 309
2.5. Stochastic equations of diffusion type with constant
coefficients 318
§3. Stability 322
3.1. Examples of stable and unstable infinite dimensional
systems 322
3.2. Stability in the mean square 327
Bibliography 333
|
| any_adam_object | 1 |
| author | Skorochod, Anatolij V. 1930-2011 |
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| bvnumber | BV003552009 |
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| discipline | Mathematik |
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| id | DE-604.BV003552009 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:01:46Z |
| institution | BVB |
| isbn | 0821845314 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002258643 |
| oclc_num | 260189402 |
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| physical | XVI, 339 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | American Mathemat. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Skorochod, Anatolij V. 1930-2011 Verfasser (DE-588)128936037 aut Asimptotičeskie metody teorii stochastičeskich differencial'nych uravnenij Asymptotic methods in the theory of stochastic differential equations A. V. Skorokhod Providence, RI American Mathemat. Soc. 1989 XVI, 339 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 78. Aus d. Russ. übers. - EST: Asimptotičeskie metody teorii stochastičeskich differencial'nych uravnenij <engl.> Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Translations of mathematical monographs 78. (DE-604)BV000002394 78. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002258643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Skorochod, Anatolij V. 1930-2011 Asymptotic methods in the theory of stochastic differential equations Translations of mathematical monographs Stochastische Differentialgleichung (DE-588)4057621-8 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4112609-9 |
| title | Asymptotic methods in the theory of stochastic differential equations |
| title_alt | Asimptotičeskie metody teorii stochastičeskich differencial'nych uravnenij |
| title_auth | Asymptotic methods in the theory of stochastic differential equations |
| title_exact_search | Asymptotic methods in the theory of stochastic differential equations |
| title_full | Asymptotic methods in the theory of stochastic differential equations A. V. Skorokhod |
| title_fullStr | Asymptotic methods in the theory of stochastic differential equations A. V. Skorokhod |
| title_full_unstemmed | Asymptotic methods in the theory of stochastic differential equations A. V. Skorokhod |
| title_short | Asymptotic methods in the theory of stochastic differential equations |
| title_sort | asymptotic methods in the theory of stochastic differential equations |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| topic_facet | Stochastische Differentialgleichung Asymptotische Entwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002258643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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