Stochastic stability of differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Ausgabe: | [softcover reprint of hardcover 2nd ed. 2012] |
| Schriftenreihe: | Stochastic modelling and applied probability
66 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russ. übers. |
| Beschreibung: | XVII, 339 S. 235 mm x 155 mm, 551 g |
| ISBN: | 9783642270284 364227028X |
Internformat
MARC
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| 100 | 1 | |a Chasʹminskij, Rafail Z. |e Verfasser |0 (DE-588)1018362622 |4 aut | |
| 240 | 1 | 0 | |a Ustojčivost' sistem differencial'nych uravnenij pri slučajnych vozmuščenijach ich parametrov |
| 245 | 1 | 0 | |a Stochastic stability of differential equations |c Rafail Khasminskii |
| 250 | |a [softcover reprint of hardcover 2nd ed. 2012] | ||
| 263 | |a 201311 | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XVII, 339 S. |c 235 mm x 155 mm, 551 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Stochastic modelling and applied probability |v 66 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 0 | 7 | |a Qualitative Theorie |0 (DE-588)4571165-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stabilität |0 (DE-588)4056693-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Exponent |0 (DE-588)4123668-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
| 689 | 0 | 1 | |a Stabilität |0 (DE-588)4056693-6 |D s |
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Datensatz im Suchindex
| _version_ | 1806330382059044864 |
|---|---|
| adam_text |
Contents
1
Boundediiess
in Probability and Stability of Stochastic Processes
Defined by Differential Equations
. 1
Í.1
Brief Review of Prerequisites from Probability Theory
. 1
1.2
Dissipative Systems of Differential Equations
. 4
J
.3
Stochastic Processes as Solutions of Differential Equations
. 9
1
.4
Boundedness in Probability of Stochastic Processes Defined by
Systems of Differential Equations
. 13
1.5
Stability
. 22
1.6
Stability of Randomly Perturbed Deterministic Systems
. 26
1.7
Estimation of a Certain Functional of a Gaussian Process
. 31
1.8
Linear Systems
. 36
2
Stationary and Periodic Solutions of Differential Equations
. 43
2.1
Stationary and Periodic Stochastic Processes. Convergence of
Stochastic Processes
. 43
2.2
Existence Conditions for Stationary and Periodic Solutions
. 46
2.3
Special Existence Conditions for Stationary and Periodic Solutions
51
2.4
Conditions for Convergence to a Periodic Solution
. 55
3
Markov Processes and Stochastic Differential Equations
. 59
3.1
Definition of Markov Processes
. 59
3.2
Stationary and Periodic Markov Processes
. 63
3.3
Stochastic Differential Equations (SDE)
. 67
3.4
Conditions for Regularity of the Solution
. , ,. 74
3.5
Stationary and Periodic Solutions of Stocrmstic Differential
Equations
. /9
3.6
Stochastic Equations and Partial Differential Equations
. 83
3.7
Conditions for Recurrence and Finiteness of Mean Recurrence Time
89
3.8
Further Conditions for Recurrence and Finiteness of Mean
Recurrence Time
. 93
Х1П
xiv
Contents
4
Ergodic Properties of Solutions of Stochastic Equations
. 99
4.1
Kolmogorov Classification of Markov Chains with Coimtably
Many Stales
. 99
4.2
Recurrence and Transience
. 101
4.3
Positive and Null Recurrent Processes
. 105
4.4
Existence of a Stationary Distribution
. 106
4.5
Strong Law of Large Numbers
.
J
09
4.6
Some Auxiliary Results
. 112
4.7
Existence of the Limit of the Transition Probability Function
. 117
4.8
Some Generalizations
. 1 19
4.9
Stabilization of the Solution of the Cauchy Problem for a
Parabolic Equation
. 122
4.10
Limit Relations for Null Recurrent Processes
. 127
4.11
Limit Relations for Null Recurrent Processes (Continued)
. 131
4.12
Alesine
Law and One Generalization
. 136
5
Stability of Stochastic Differential Equations
.145
5.1
Statement of the Problem
. 145
5.2
Some Auxiliary Results
. 148
5.3
Stability in Probability
. 352
5.4
Asymptotic
Stability
in Probability and Instability
. 155
5.5
Examples
. 159
5.6
Differentiability of Solutions of Stochastic Equations with
Respect to the Initial Conditions
.165
5.7
Exponential /^-Stability and ¿^-Instability
., , 171
5.8
Almost Sure Exponential Stability
.175
6
Systems of Linear Stochastic Equations
.177
6.1
One-Dimensional Systems
. 177
6.2
Equations for Moments
. 182
6.3
Exponential p-Stability and ¿/-Instability
. 184
6.4
Exponential ¿»-Stability and
q
-Instability (Continued)
.
і
88
6.5
Uniform Stability in the Large
. 192
6.6
Stability of Products of Independent Matrices
. 196
6.7
Asymptotic Stability of Linear Systems with Constant Coefficients
201
6.8
Systems with Constant Coefficients (Continued)
. 206
6.9
Two Examples
. 211
6.10
«-th Order Equations
. 216
6.11
Stochastic Stability in the Strong and Weak Senses
. 223
7
Some Special Problems in the Theory of Stability of SDK's
.227
7.1
Stability in the First Approximation
.227
7.2
Instability in the First Approximation
.229
7.3
Two Examples
.231
7.4
Stability Under Damped Random Perturbations
.234
7.5
Application to Stochastic
Approximation.237
Contents xv
7 6
Stochastic Approximations when the Regression Equation Has
Several Roots
. 239
7.7
Some Generalizations
.245
7.7.
J
Stability and Excessive Functions
. 245
7.7.2
Stability of the Invariant Set
. 247
7.7.3
Equations Whose Coefficients Are Markov Processes
. . . 247
7.7.4
Stability Under Persistent Perturbation by White Noise
. . 249
7.7.5
Boundedness in Probability of the Output Process of a
Nonlinear Stochastic System
. 25 1
S
Stabilization of Controlled Stochastic Systems (This chapter was
written jointly with M.B. Nevelson)
. 253
8.1
Preliminary Remarks
. 253
8.2
Bellman's Principle
. 254
8.3
Linear Systems
. 258
8.4
Method of Successive Approximations
. 260
Appendix A Appendix to the First English Edition
. 265
A. I Moment Stability and Almost Sure Stability for Linear Systems
of Equations Whose Coefficients are Markov Processes
. 265
A.
2
Almost Sure Stability of the Paths of One Dimensional Diffusion
Processes
. 269
A.3 Reduction Principle
. 2/5
A.4 Some Further Results
. 279
Appendix
В
Appendix to the Second Edition. Moment Lyapunov
Exponents and Stability Index (Written jointly with G.N. Milstein)
281
B.I Preliminaries
. 281
B.2 Basic Theorems
. 285
B.2.1 Nondegeneracy Conditions
. 285
B.2.
2
Semigroups of Positive Compact Operators and Moment
Lyapunov Exponents
. 286
B.2.3 Generator of the Process A
. 294
B.2.4 Generator of Semigroup Tt(p)
f
(λ).
296
В.
2.5
Various Representations of Semigroup
rř
(/?)ƒ
(λ)
. 299
В.
3
Stability Index
. 303
В.
3.1
Stability Index for Linear Stochastic Differential Equations
303
B.3.2 Stability Index for Nonlinear SDEs
. 305
B.4 Moment Lyapunov Exponent and Stability Index for System with
Small Noise
. 309
B.4.1 Introduction and Statement of Problem
. 309
B.4.
2
Method of Asymptotic Expansion
, ,. . 312
B.4.3 Stability Index
. 3 16
B.4.
4
Applications
. 319
References
. 323
. 335 |
| any_adam_object | 1 |
| author | Chasʹminskij, Rafail Z. |
| author_GND | (DE-588)1018362622 |
| author_facet | Chasʹminskij, Rafail Z. |
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| author_sort | Chasʹminskij, Rafail Z. |
| author_variant | r z c rz rzc |
| building | Verbundindex |
| bvnumber | BV042325563 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)903413106 (DE-599)DNB1048740315 |
| discipline | Mathematik |
| edition | [softcover reprint of hardcover 2nd ed. 2012] |
| format | Book |
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| id | DE-604.BV042325563 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T02:08:11Z |
| institution | BVB |
| isbn | 9783642270284 364227028X |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027762405 |
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| physical | XVII, 339 S. 235 mm x 155 mm, 551 g |
| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | Springer |
| record_format | marc |
| series | Stochastic modelling and applied probability |
| series2 | Stochastic modelling and applied probability |
| spelling | Chasʹminskij, Rafail Z. Verfasser (DE-588)1018362622 aut Ustojčivost' sistem differencial'nych uravnenij pri slučajnych vozmuščenijach ich parametrov Stochastic stability of differential equations Rafail Khasminskii [softcover reprint of hardcover 2nd ed. 2012] 201311 Berlin [u.a.] Springer 2013 XVII, 339 S. 235 mm x 155 mm, 551 g txt rdacontent n rdamedia nc rdacarrier Stochastic modelling and applied probability 66 Aus dem Russ. übers. Qualitative Theorie (DE-588)4571165-3 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Ljapunov-Exponent (DE-588)4123668-3 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Stabilität (DE-588)4056693-6 s DE-604 Qualitative Theorie (DE-588)4571165-3 s Ljapunov-Exponent (DE-588)4123668-3 s 1\p DE-604 Stochastic modelling and applied probability 66 (DE-604)BV019623501 66 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4618454&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027762405&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Chasʹminskij, Rafail Z. Stochastic stability of differential equations Stochastic modelling and applied probability Qualitative Theorie (DE-588)4571165-3 gnd Stabilität (DE-588)4056693-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd |
| subject_GND | (DE-588)4571165-3 (DE-588)4056693-6 (DE-588)4057621-8 (DE-588)4123668-3 |
| title | Stochastic stability of differential equations |
| title_alt | Ustojčivost' sistem differencial'nych uravnenij pri slučajnych vozmuščenijach ich parametrov |
| title_auth | Stochastic stability of differential equations |
| title_exact_search | Stochastic stability of differential equations |
| title_full | Stochastic stability of differential equations Rafail Khasminskii |
| title_fullStr | Stochastic stability of differential equations Rafail Khasminskii |
| title_full_unstemmed | Stochastic stability of differential equations Rafail Khasminskii |
| title_short | Stochastic stability of differential equations |
| title_sort | stochastic stability of differential equations |
| topic | Qualitative Theorie (DE-588)4571165-3 gnd Stabilität (DE-588)4056693-6 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Ljapunov-Exponent (DE-588)4123668-3 gnd |
| topic_facet | Qualitative Theorie Stabilität Stochastische Differentialgleichung Ljapunov-Exponent |
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| volume_link | (DE-604)BV019623501 |
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