Stochastic analysis on manifolds:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Schriftenreihe: | Graduate studies in mathematics
Volume 38 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 281 S. |
| ISBN: | 9780821808023 0821808028 |
Internformat
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| 245 | 1 | 0 | |a Stochastic analysis on manifolds |c Elton P. Hsu |
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| 830 | 0 | |a Graduate studies in mathematics |v Volume 38 |w (DE-604)BV009739289 |9 38 | |
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Datensatz im Suchindex
| _version_ | 1819351796825456640 |
|---|---|
| adam_text | Contents
Preface xiii
Introduction 1
Chapter 1. Stochastic Differential Equations and Diffusions 5
§1.1. SDE on euclidean space 6
§1.2. SDE on manifolds 19
§1.3. Diffusion processes 24
Chapter 2. Basic Stochastic Differential Geometry 35
§2.1. Frame bundle and connection 36
§2.2. Tensor fields 41
§2.3. Horizontal lift and stochastic development 44
§2.4. Stochastic line integrals 51
§2.5. Martingales on manifolds 55
§2.6. Martingales on submanifolds 60
Chapter 3. Brownian Motion on Manifolds 71
§3.1. Laplace Beltrami operator 72
§3.2. Brownian motion on manifolds 78
§3.3. Examples of Brownian motion 82
§3.4. Distance function 88
§3.5. Radial process 92
§3.6. An exit time estimate 98
Chapter 4. Brownian Motion and Heat Semigroup 101
ix
x Contents
§4.1. Heat kernel as transition density function 102
§4.2. Stochastic completeness 107
§4.3. Co property of the heat semigroup 112
§4.4. Recurrence and transience 117
§4.5. Comparison of heat kernels 127
Chapter 5. Short time Asymptotics 129
§5.1. Short time asymptotics: near points 130
§5.2. Varadhan s asymptotic relation 133
§5.3. Short time asymptotics: distant points 137
§5.4. Brownian bridge 142
§5.5. Derivatives of the logarithmic heat kernel 147
Chapter 6. Further Applications 157
§6.1. Dirichlet problem at infinity 158
§6.2. Constant upper bound 166
§6.3. Vanishing upper bound 168
§6.4. Radially symmetric manifolds 172
§6.5. Coupling of Brownian motion 179
§6.6. Coupling and index form 182
§6.7. Eigenvalue estimates 186
Chapter 7. Brownian Motion and Index Theorems 191
§7.1. Weitzenbock formula 192
§7.2. Heat equation on differential forms 198
§7.3. Gauss Bonnet Chern formula 201
§7.4. Clifford algebra and spin group 208
§7.5. Spin bundle and the Dirac operator 213
§7.6. Atiyah Singer index theorem 217
§7.7. Brownian holonomy 222
Chapter 8. Analysis on Path Spaces 229
§8.1. Quasi invariance of the Wiener measure 230
§8.2. Flat path space 234
§8.3. Gradient formulas 246
§8.4. Integration by parts in path space 250
§8.5. Martingale representation theorem 256
§8.6. Logarithmic Sobolev inequality and hypercontractivity 258
Contents xi
§8.7. Logarithmic Sobolev inequality on path space 263
Notes and Comments 267
General Notations 271
Bibliography 275
Index 279
|
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| author | Hsu, Elton P. 1959- |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514.74 |
| dewey-search | 514.74 |
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| id | DE-604.BV013265766 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:44:13Z |
| institution | BVB |
| isbn | 9780821808023 0821808028 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009043652 |
| oclc_num | 248316848 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 DE-11 DE-188 |
| physical | XIV, 281 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spellingShingle | Hsu, Elton P. 1959- Stochastic analysis on manifolds Graduate studies in mathematics Differenzierbare Mannigfaltigkeit - Stochastische Analysis Differentialgeometrie (DE-588)4012248-7 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4057621-8 (DE-588)4274463-5 |
| title | Stochastic analysis on manifolds |
| title_auth | Stochastic analysis on manifolds |
| title_exact_search | Stochastic analysis on manifolds |
| title_full | Stochastic analysis on manifolds Elton P. Hsu |
| title_fullStr | Stochastic analysis on manifolds Elton P. Hsu |
| title_full_unstemmed | Stochastic analysis on manifolds Elton P. Hsu |
| title_short | Stochastic analysis on manifolds |
| title_sort | stochastic analysis on manifolds |
| topic | Differenzierbare Mannigfaltigkeit - Stochastische Analysis Differentialgeometrie (DE-588)4012248-7 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| topic_facet | Differenzierbare Mannigfaltigkeit - Stochastische Analysis Differentialgeometrie Stochastische Differentialgleichung Diffusionsprozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009043652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT hsueltonp stochasticanalysisonmanifolds |