Stochastic PDE's and Kolmogorov equations in infinite dimensions: lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Series: | Lecture notes in mathematics
1715 : Subseries Fondazione CIME Centro Internazionale Matematico Estivo <Firenze>: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) 1998,2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 239 S. |
| ISBN: | 3540665455 |
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| 245 | 1 | 0 | |a Stochastic PDE's and Kolmogorov equations in infinite dimensions |b lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 |c N. V. Krylov ... Ed.: G. Da Prato |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a VIII, 239 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1715 : Subseries Fondazione CIME | |
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| 650 | 4 | |a Processus de diffusion | |
| 650 | 4 | |a Processus gaussiens | |
| 650 | 4 | |a Équations aux dérivées partielles stochastiques | |
| 650 | 4 | |a Diffusion processes | |
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Record in the Search Index
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| adam_text | Table of Contents
Preface V
On Kolmogorov s equations for finite dimensional diffusions
N.V. Krylov 1
1. Solvability of Ito s stochastic equations 1
2. Markov property of solutions 8
2.1 Regular equations 8
2.2 Some properties of Euler s approximations 11
2.3 Markov property 15
3. Conditional version of Kolmogorov s equation 16
4. Differentiability of solutions of stochastic equations with respect to
initial data 21
4.1 Estimating moments of solutions of Ito s equations 22
4.2 Smoothness of solutions depending on a parameter 26
4.3 Estimating moments of derivatives of solutions 31
4.4 The notions of L continuity and L differentiability 33
4.5 Differentiability of certain expectations depending on a parameter 36
5. Kolmogorov s equation in the whole space 42
5.1 Stratified equations 43
5.2 Sufficient conditions for regularity 46
5.3 Kolmogorov s equation 48
6. Some integral approximations of differential operators 53
7. Kolmogorov s equations in domains 58
Lp—analysis of finite and infinite dimensional diffusion
operators
Michael Rockner 65
1. Introduction 65
2. Solution of Kolmogorov equations via sectorial forms 66
2.1 Preliminaries 66
2.2 Sectorial forms 68
2.3 Sectorial forms on L2(E m) 70
2.4 Examples and Applications 72
Table of Contents VII
3. Symmetrizing measures 78
3.1 The classical finite dimensional case 78
3.2 Representation of symmetric diffusion operators 80
3.3 Ornstein Uhlenbeck type operators 81
3.4 Operators with non linear drift 83
4. Non sectorial cases: perturbations by divergence free vector fields .. 86
4.1 Diffusion operators on LP(E; m) 86
4.2 Solution of Kolmogorov equations on£ (fi;m) 88
4.3 Uniqueness problem 92
4.4 Concluding remarks 95
5. Invariant measures: regularity, existence and uniqueness 96
5.1 Sectorial case 96
5.2 Non sectorial cases 99
6. Corresponding diffusions and relation to Martingale problems 103
6.1 Existence of associated diffusions 103
6.2 Solution of the martingale problem 105
6.3 Uniqueness 105
7. Appendix 106
7.1 Kolmogorov equations in L2 (E; /i) for infinite dimensional man¬
ifolds E: a case study from continuum statistical mechanics ... 106
7.2 Ergodicity 110
Parabolic equations on Hilbert spaces
J. Zabczyk 117
1. Preface 117
2. Preliminaries 119
2.1 Linear operators 119
2.2 Measures and random variables 123
2.3 Wiener process and stochastic equations 127
3. Heat Equation 130
3.1 Introduction 131
3.2 Regular initial functions 135
3.3 Gross Laplacian 137
3.4 Heat equation with general initial functions 139
3.5 Generators of the heat semigroups 143
3.6 Nonparabolicity 147
4. Transition semigroups 149
4.1 Transition semigroups in the space of continuous functions .... 150
4.2 Transition semigroups in spaces of square summable functions . 154
5. Heat equation with a first order term 157
5.1 Introduction 158
5.2 Regular initial functions 159
5.3 General initial functions 163
5.4 Range condition and examples 170
VIII Table of Contents
6. General parabolic equations. Regularity 174
6.1 Convolution type and evaluation maps 174
6.2 Solutions of stochastic equations 178
6.3 Space and time regularity of generalized solutions 179
6.4 Strong Feller property 181
7. General parabolic equations. Uniqueness 186
7.1 Uniqueness for the heat equation 186
7.2 Uniqueness in the general case 187
8. Parabolic equations in open sets 191
8.1 Introduction 191
8.2 Main theorem 192
8.3 Estimates of the exit probabilities 195
9. Applications 198
9.1 HJB equation of stochastic control 198
9.2 Solvability of HJB equation 202
9.3 Kolmogorov s equation in mathematical finance 204
10. Appendix 206
10.1 Implicit function theorems 206
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| indexdate | 2024-07-09T18:33:10Z |
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| language | English |
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| physical | VIII, 239 S. |
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| series | Lecture notes in mathematics Centro Internazionale Matematico Estivo <Firenze>: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) |
| series2 | Lecture notes in mathematics Centro Internazionale Matematico Estivo <Firenze>: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) |
| spelling | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 N. V. Krylov ... Ed.: G. Da Prato Berlin [u.a.] Springer 1999 VIII, 239 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1715 : Subseries Fondazione CIME Centro Internazionale Matematico Estivo <Firenze>: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) 1998,2 Equacoes diferenciais parciais larpcal Kolmogorov-integralen gtt Oneindige dimensie gtt Partiële differentiaalvergelijkingen gtt Processus de diffusion Processus gaussiens Équations aux dérivées partielles stochastiques Diffusion processes Gaussian processes Stochastic partial differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Kolmogorovsche Differentialgleichungen (DE-588)4164698-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1998 Cetraro gnd-content Stochastische partielle Differentialgleichung (DE-588)4135969-0 s Kolmogorovsche Differentialgleichungen (DE-588)4164698-8 s DE-604 Krylov, Nikolaj V. 1941- Sonstige (DE-588)121699684 oth Da Prato, Giuseppe 1936-2023 Sonstige (DE-588)121352641 oth Lecture notes in mathematics 1715 : Subseries Fondazione CIME (DE-604)BV000676446 1715 Centro Internazionale Matematico Estivo <Firenze>: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) 1998,2 (DE-604)BV000903443 1998,2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 Lecture notes in mathematics Centro Internazionale Matematico Estivo <Firenze>: Lectures given at the ... session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Equacoes diferenciais parciais larpcal Kolmogorov-integralen gtt Oneindige dimensie gtt Partiële differentiaalvergelijkingen gtt Processus de diffusion Processus gaussiens Équations aux dérivées partielles stochastiques Diffusion processes Gaussian processes Stochastic partial differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Kolmogorovsche Differentialgleichungen (DE-588)4164698-8 gnd |
| subject_GND | (DE-588)4135969-0 (DE-588)4164698-8 (DE-588)1071861417 |
| title | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 |
| title_auth | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 |
| title_exact_search | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 |
| title_full | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 N. V. Krylov ... Ed.: G. Da Prato |
| title_fullStr | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 N. V. Krylov ... Ed.: G. Da Prato |
| title_full_unstemmed | Stochastic PDE's and Kolmogorov equations in infinite dimensions lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 N. V. Krylov ... Ed.: G. Da Prato |
| title_short | Stochastic PDE's and Kolmogorov equations in infinite dimensions |
| title_sort | stochastic pde s and kolmogorov equations in infinite dimensions lectures given at the 2nd session of the centro internazionale matematico estivo cime held in cetraro italy august 24 september 1 1998 |
| title_sub | lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998 |
| topic | Equacoes diferenciais parciais larpcal Kolmogorov-integralen gtt Oneindige dimensie gtt Partiële differentiaalvergelijkingen gtt Processus de diffusion Processus gaussiens Équations aux dérivées partielles stochastiques Diffusion processes Gaussian processes Stochastic partial differential equations Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Kolmogorovsche Differentialgleichungen (DE-588)4164698-8 gnd |
| topic_facet | Equacoes diferenciais parciais Kolmogorov-integralen Oneindige dimensie Partiële differentiaalvergelijkingen Processus de diffusion Processus gaussiens Équations aux dérivées partielles stochastiques Diffusion processes Gaussian processes Stochastic partial differential equations Stochastische partielle Differentialgleichung Kolmogorovsche Differentialgleichungen Konferenzschrift 1998 Cetraro |
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| volume_link | (DE-604)BV000676446 (DE-604)BV000903443 |
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