Stochastic flows and stochastic differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 1. paperback ed. |
| Series: | Cambridge studies in advanced mathematics
24 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 346 S. |
| ISBN: | 9780521599252 0521350506 0521599253 |
Staff View
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Record in the Search Index
| _version_ | 1804126098626183168 |
|---|---|
| adam_text | STOCHASTIC FLOW S AND STOCHASTIC DIFFERENTIAL EQUATIONS HIROSHI KUNITA
PROFESSOR, DEPARTMENT OF APPLIED SCIENCE, KYUSHU UNIVERSITY JGF
CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE XI 1 STOCHASTIC PROCESSES
AND RANDOM FIELDS 1 1.1 PRELIMINARIES 1 PROBABILITY SPACES AND RANDOM
VARIABLES 1 CONDITIONAL EXPECTATIONS 4 1.2 STOCHASTIC PROCESSES 5
BROWNIAN MOTIONS 5 MARTINGALES 6 MARKOV PROCESSES 9 1.3 ERGODIC
PROPERTIES OF MARKOV PROCESSES 15 RECURRENT AND TRANSIENT PROCESSES 15
ERGODIC PROPERTIES 21 ERGODIC THEOREMS 25 POTENTIAL KERNEIS 28 1.4
RAHDOM FIELDS 31 KOLMOGOROV S CONTINUITY CRITERION OF RANDOM FIELDS 31
WEAK CONVERGENCE OF CONTINUOUS RANDOM FIELDS 37 KOLMOGOROV S TIGHTNESS
CRITERION 38 2 CONTINUOUS SEMIMARTINGALES AND STOCHASTIC INTEGRALS 43
2.1 PRELIMINARIES 43 LOCALMARTINGALES AND SEMIMARTINGALES 43 LOCAL
SEMIMARTINGALES 45 2.2 QUADRATIC VARIATIONAL PROCESSES 46 QUADRATIC
VARIATIONS OF CONTINUOUS SEMIMARTINGALES 46 JOINT QUADRATIC VARIATIONS
52 CONTINUITY OF QUADRATIC VARIATIONS 53 2.3 STOCHASTIC INTEGRALS AND
ITOE S FORMULA 56 ITOE S INTEGRALS AND STRATONOVICH S INTEGRALS 56
ORTHOGONAL DECOMPOSITION OF LOCALMARTINGALES 61 ITOE S FORMULA - 64
APPLICATIONS OF ITOE S FORMULA 66 3 SEMIMARTINGALES WITH SPATIAL
PARAMETERS AND STOCHASTIC INTEGRALS 71 3.1 PRELIMINARIES 71 MARTINGALES
WITH SPATIAL PARAMETERS 71 REGULARITY OF MARTINGALES WITH RESPECT TO
SPATIAL PARAMETERS 74 VIII CONTENTS 3.2 STOCHASTIC INTEGRALS BASED ON
SEMIMARTINGALES WITH SPATIAL PARAMETERS 79 ITOE INTEGRALS: CASE OF
MARTINGALES 79 ITOE INTEGRALS: CASE OF SEMIMARTINGALES 84 STRATONOVICH
INTEGRALS 86 TIME CHANGE OF STOCHASTIC INTEGRALS 88 CASE OF LOCAL
SEMIMARTINGALES 90 3.3 SOME FORMULAS FOR STOCHASTIC INTEGRALS 92
GENERALIZED ITOE S FORMULA 92 INTEGRAL AND DIFFERENTIAL RULES FOR
STOCHASTIC INTEGRALS 94 3.4 STOCHASTIC DIFFERENTIAL EQUATIONS 100 ITOE S
STOCHASTIC DIFFERENTIAL EQUATION 100 EXISTENCE AND UNIQUENESS OF THE
SOLUTION 101 EXAMPLE 106 LOCAL SOLUTION 107 STRATONOVICH S STOCHASTIC
DIFFERENTIAL EQUATION 110 BACKWARD INTEGRALS AND BACKWARD EQUATIONS 111
4 STOCHASTIC FLOWS 114 4.1 PRELIMINARIES 114 4.2 BROWNIAN FLOWS 119
N-POINT MOTIONS OF BROWNIAN FLOWS 119 INFINITESIMAL MEANS AND
COVARIANCES 120 FORWARD RANDOM INFINITESIMAL GENERATORS 128 BACKWARD
RANDOM INFINITESIMAL GENERATORS 130 4.3 ASYMPTOTIC PROPERTIES OF
BROWNIAN FLOWS 134 MEASURE PRESERVING BROWNIAN FLOW 134 ASYMPTOTIC
BEHAVIOR OF (P T ~ L (U) 140 ASYMPTOTIC BEHAVIOR OF (P,(U) 144 4.4
SEMIMARTINGALE FLOWS 147 RANDOM INFINITESIMAL GENERATORS 147 ITOE S
FORMULAS FOR STOCHASTIC FLOWS 151 4.5 HOMEOMORPHIC PROPERTY OF SOLUTIONS
OF SDE 154 CONSTRUCTION OF STOCHASTIC FLOWS 154 L -ESTIMATES OF
SOLUTIONS 156 HOMEOMORPHIC PROPERTY 159 4.6 DIFFEOMORPHIC PROPERTY OF
SOLUTIONS OF SDE 164 DIFFERENTIABILITY OF SOLUTIONS 164 DIFFEOMORPHIC
PROPERTY 173 4.7 STOCHASTIC FLOWS OF LOCAL DIFFEOMORPHISMS 176
CONSTRUCTION OF STOCHASTIC FLOWS OF LOCAL DIFFEOMORPHISMS 176 GLOBAL
STOCHASTIC FLOWS 180 RANDOM INFINITESIMAL GENERATORS 184 4.8 STOCHASTIC
FLOWS ON MANIFOLDS 185 PRELIMINARIES 185 STOCHASTIC DIFFERENTIAL
EQUATIONS ON MANIFOLDS 188 DIFFEOMORPHIC PROPERTY OF SOLUTIONS 192 IX
RANDOM INFINITESIMAL GENERATORS 195 ITOE S FORMULAS FOR STOCHASTIC FLOWS
ON MANIFOLDS 198 4.9 ITOE S FORMULAS FOR STOCHASTIC FLOWS AND THEIR
APPLICATIONS 201 ITOE S FORMULA FOR
M ACTING ON VECTOR FIELDS 201 ITOE S FORMULA FOR
S , ACTING ON TENSOR FIELDS 204 COMPOSITION AND DECOMPOSITION OF THE
SOLUTION 208 SUPPORTS OF STOCHASTIC FLOWS OF DIFFEOMORPHISMS 214 5
CONVERGENCE OF STOCHASTIC FLOWS 218 5.1 PRELIMINARIES 218 5.2
CONVERGENCE AS DIFFUSIONS I 221 A CONVERGENCE THEOREM 221 UNIFORM
L -ESTIMATES 223 SEMIMARTINGALE CHARACTERIZATION OF THE LIMIT MEASURE
225 PROOF OF THEOREM 5.2.1 231 STRONG CONVERGENCE 232 5.3 CONVERGENCE AS
DIFFUSIONS II 234 STATEMENTS OF THEOREMS 234 UNIFORM L P -ESTIMATES 238
CHARACTERIZATION OF THE LIMIT MEASURE 240 5.4 CONVERGENCE AS STOCHASTIC
FLOWS 244 CONVERGENCE AS O -FLOWS 244 UNIFORM L -ESTIMATE OF STOCHASTIC
FLOWS 247 PROOF OF LEMMA 5.4.4 250 CONVERGENCE AS G^-FLOWS 255 5.5
EXTENSIONSOF CONVERGENCE THEOREMS 258 EXTENSIONS OF CONVERGENCE THEOREMS
AS DIFFUSIONS 258 EXTENSIONS OF CONVERGENCE THEOREMS AS STOCHASTIC FLOWS
261 5.6 SOME LIMIT THEOREMS FOR STOCHASTIC DIFFERENTIAL EQUATIONS 262
CENTRAL LIMIT THEOREM FOR STOCHASTIC FLOWS. I MIXING CASE 262 CENTRAL
LIMIT THEOREM FOR STOCHASTIC FLOWS. II MARKOV CASE 270 5.7
APPROXIMATIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS, SUPPORTS OF
STOCHASTIC FLOWS 274 PRELIMINARIES 274 A WEAK APPROXIMATION THEOREM 275
STRONG APPROXIMATION THEOREMS 281 SUPPORTS OF STOCHASTIC FLOWS 282 6
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS 28 6 6.1 FIRST ORDER
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS 286 PRELIMINARIES 286
STOCHASTIC CHARACTERISTIC SYSTEM 288 EXISTENCE AND UNIQUENESS OF
SOLUTIONS 291 QUASI-LINEAR AND SEMI-LINEAR EQUATIONS 294 LINEAR
EQUATIONS 297 6.2 SECOND ORDER STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
301 PRELIMINARIES 301 X CONTENTS EXISTENCE AND UNIQUENESS OF SOLUTIONS
PROBABILISTIC REPRESENTATION OF SOLUTIONS ADJOINT EQUATION APPLICATIONS
TO NONLINEAR FILTERING THEORY FILTERING PROBLEM STOCHASTIC PARTIAL
DIFFERENTIAL EQUATIONS FOR NONLINEAR FILTER ROBUSTNESS OF NONLINEAR
FILTER KAIMAN FILTER LIMIT THEOREMS FOR STOCHASTIC PARTIAL DIFFERENTIAL
EQUATIONS STATEMENT OF THEOREMS PROOF OF THEOREMS FREQUENTLY USED
NOTATION AND ASSUMPTIONS REMARKS ON REFERENCES REFERENCES INDEX 304 307
310 315 315 318 322 323 326 326 32? 334 336 340 345
|
| any_adam_object | 1 |
| author | Kunita, H. 1937-2019 |
| author_GND | (DE-588)1055753419 |
| author_facet | Kunita, H. 1937-2019 |
| author_role | aut |
| author_sort | Kunita, H. 1937-2019 |
| author_variant | h k hk |
| building | Verbundindex |
| bvnumber | BV011573111 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.2 |
| callnumber-search | QA274.2 |
| callnumber-sort | QA 3274.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)36864963 (DE-599)BVBBV011573111 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV011573111 |
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| indexdate | 2024-07-09T18:12:03Z |
| institution | BVB |
| isbn | 9780521599252 0521350506 0521599253 |
| language | English |
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| physical | XIV, 346 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Kunita, H. 1937-2019 Verfasser (DE-588)1055753419 aut Stochastic flows and stochastic differential equations Hiroshi Kunita 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 1997 XIV, 346 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 24 DIFFERENTIAL EQUATIONS nasat PARTIAL DIFFERENTIAL EQUATIONS nasat STOCHASTIC PROCESSES nasat Flows (Differentiable dynamical systems) Stochastic analysis Stochastic differential equations Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Strömung (DE-588)4195753-2 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Stochastische Strömung (DE-588)4195753-2 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Cambridge studies in advanced mathematics 24 (DE-604)BV000003678 24 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007792662&sequence=000001&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 | Kunita, H. 1937-2019 Stochastic flows and stochastic differential equations Cambridge studies in advanced mathematics DIFFERENTIAL EQUATIONS nasat PARTIAL DIFFERENTIAL EQUATIONS nasat STOCHASTIC PROCESSES nasat Flows (Differentiable dynamical systems) Stochastic analysis Stochastic differential equations Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastische Strömung (DE-588)4195753-2 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4057621-8 (DE-588)4195753-2 |
| title | Stochastic flows and stochastic differential equations |
| title_auth | Stochastic flows and stochastic differential equations |
| title_exact_search | Stochastic flows and stochastic differential equations |
| title_full | Stochastic flows and stochastic differential equations Hiroshi Kunita |
| title_fullStr | Stochastic flows and stochastic differential equations Hiroshi Kunita |
| title_full_unstemmed | Stochastic flows and stochastic differential equations Hiroshi Kunita |
| title_short | Stochastic flows and stochastic differential equations |
| title_sort | stochastic flows and stochastic differential equations |
| topic | DIFFERENTIAL EQUATIONS nasat PARTIAL DIFFERENTIAL EQUATIONS nasat STOCHASTIC PROCESSES nasat Flows (Differentiable dynamical systems) Stochastic analysis Stochastic differential equations Stochastischer Prozess (DE-588)4057630-9 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Stochastische Strömung (DE-588)4195753-2 gnd |
| topic_facet | DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS STOCHASTIC PROCESSES Flows (Differentiable dynamical systems) Stochastic analysis Stochastic differential equations Stochastischer Prozess Stochastische Differentialgleichung Stochastische Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007792662&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT kunitah stochasticflowsandstochasticdifferentialequations |