New directions in Dirichlet forms:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Providence, RI
American Math. Soc. [u.a.]
1998
|
| Series: | American Mathematical Society: AMS, IP studies in advanced mathematics
8 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 277 S. |
| ISBN: | 0821810618 |
Staff View
MARC
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| 245 | 1 | 0 | |a New directions in Dirichlet forms |c Jürgen Jost ... |
| 264 | 1 | |a Providence, RI |b American Math. Soc. [u.a.] |c 1998 | |
| 300 | |a XIV, 277 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a American Mathematical Society: AMS, IP studies in advanced mathematics |v 8 | |
| 650 | 7 | |a Dirichlet-vormen |2 gtt | |
| 650 | 7 | |a Probabilités |2 ram | |
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Record in the Search Index
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| adam_text | Contents
Jiirgen Jost: Nonlinear Dirichlet Forms 1
1.1 Introduction 1
1.2 Definition and properties of generalized
Dirichlet forms 3
1.3 Resolvents, semigroups, and variational
aspects 10
1.4 Convergence properties 24
1.5 Generalized harmonic maps 28
1.6 Appendix: Geometric notions 41
Wilfrid S. Kendall: From Stochastic Parallel Transport to Har¬
monic Maps 49
2.1 Introduction 49
2.1.1 Aim and objectives 49
2.1.2 History and motivation 49
2.1.3 Stochastic calculus formalism 51
2.2 Stochastic differential geometry 56
2.2.1 Intrinsic approach to semimartingales 56
2.2.2 Lifting to the frame bundle 56
2.2.3 The semimartingale zoo 59
2.2.4 Intrinsic geometry 68
2.2.5 Diffusions and statistical shape 69
2.2.6 Geodesic variational formulae 69
2.2.7 Distance from a fixed point 70
2.2.8 Distance between two moving points (I) 71
2.2.9 Distance between two moving points (II) 71
2.3 Distance and semimartingales 72
2.3.1 Distance of a F martingale from a point 73
vii
viii CONTENTS
2.3.2 Probabilistic approaches to Picard theorems 74
2.3.3 F martingale convergence theorem 76
2.3.4 An Ultimate Liouville Theorem 77
2.3.5 Picard little theorem for harmonic maps 79
2.3.6 Limiting directions for Brownian motion 79
2.3.7 Probabilistic proofs for Picard little theorems 81
2.3.8 Life on the cut locus 83
2.3.9 Historical perspective 83
2.3.10 Cut locus correction by upper bound 84
2.4 Coupling and parallel transport 85
2.4.1 Distance between two F martingales 87
2.4.2 Coupling Brownian motions in the case of nonnegative
Ricci curvature 89
2.4.3 Applications 92
2.5 Harmonic map Dirichlet problem 94
2.5.1 The role of convexity and coupling 94
2.5.2 Construction of F martingales 96
2.5.3 Existence using barycentres 97
2.5.4 Other approaches 99
2.5.5 Smoothness via gradient estimates 100
2.5.6 Equivalences 101
Umberto Mosco: Dirichlet forms and self—similarity 117
3.1 Introduction 117
3.2 Self similar fractals 120
3.3 Variational fractals 124
3.4 The Lagrangian metrics 129
3.5 The intrinsic homogeneous structure 134
3.6 Field operators and spectral asymptotics 136
3.7 Local solutions 139
3.8 Scaled Poincare inequalities 143
3.9 Nash inequalities and Morrey Sobolev imbeddings 147
Michael Rockner: Stochastic analysis on configuration spaces: ba¬
sic ideas and recent results 157
4.1 Introduction 157
4.2 Lifting the geometry from the base manifold to the configuration
space 159
CONTENTS ix
4.2.1 Test functions, flows, directional derivatives 161
4.2.2 Tangent bundle, gradient, vector fields and divergence . . 161
4.2.3 Characterization of the volume elements as the mixed
Poisson measures 163
4.2.4 Laplacian and classical pre Dirichlet form 168
4.3 Infinite dimensional analysis and Brownian motion on configura¬
tion spaces 169
4.3.1 Dirichlet forms and operators 169
4.3.2 Markov uniqueness, essential self adjointness and heat
semigroup 171
4.3.3 Brownian motion 179
4.3.4 Ergodicity in the free case 183
4.4 Classical Dirichlet forms on configuration spaces w.r.t. general
measures 184
4.4.1 Closability, domains and Sobolev spaces 185
4.4.2 Quasi regularity and corresponding diffusions 190
4.5 Intrinsic metric on configuration spaces 193
4.5.1 Identification of the intrinsic metric for a class of measures 194
4.5.2 A Rademacher theorem 194
4.5.3 Potential theoretic consequences 195
4.6 Gibbs measures on configuration spaces 196
4.6.1 Grand canonical Gibbs measures 197
4.6.2 Canonical Gibbs measures 199
4.6.3 Closability of the corresponding Dirichlet forms 201
4.7 Integration by parts characterization of canonical Gibbs measures 209
4.7.1 Ruelle measures 210
4.7.2 Integration by parts characterization . . . 213
4.8 Infinite interacting particle systems 216
4.8.1 Stochastic dynamics corresponding to Gibbs states . . . 216
4.8.2 Solutions of the martingale problem resp. of the corre¬
sponding heuristic SDE 217
4.9 Ergodicity 218
4.9.1 A general result on irreducibility resp. ergodicity .... 219
4.9.2 Applications to canonical Gibbs and Ruelle measures . . 222
Karl Theodor Sturm: The Geometric Aspect of Dirichlet Forms 233
5.1 Introduction 233
5.2 Estimates for Semigroups and Resolvents 235
x CONTENTS
5.2.1 The Dirichlet Form 236
5.2.2 Estimates for the Semigroup 237
5.2.3 Estimates for the Resolvent 240
5.3 Capacity Estimates and Applications 240
5.3.1 Basic Properties of Quasi regular Dirichlet Forms .... 241
5.3.2 The Capacity Estimate 245
5.3.3 Criteria for Polarity 249
5.3.4 Criteria for Recurrence and Transience 252
5.4 The Intrinsic Metric 255
5.4.1 Basic Properties of the Intrinsic Metric 255
5.4.2 Global Form Properties and Geometry at Infinity .... 258
5.5 Examples 260
5.5.1 The Laplacian on RN 260
5.5.2 Laplacians with Weights 261
5.5.3 Elliptic and Subelliptic Operators on JRN 267
5.5.4 Laplace Beltrami Operators on Riemannian Manifolds . 268
|
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| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SD 1997 SK 560 |
| ctrlnum | (OCoLC)39189961 (DE-599)BVBBV013365635 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Konferenzschrift 1997 Anogeia |
| id | DE-604.BV013365635 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:44:34Z |
| institution | BVB |
| isbn | 0821810618 |
| language | English |
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| physical | XIV, 277 S. |
| publishDate | 1998 |
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| publisher | American Math. Soc. [u.a.] |
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| series | American Mathematical Society: AMS, IP studies in advanced mathematics |
| series2 | American Mathematical Society: AMS, IP studies in advanced mathematics |
| spelling | New directions in Dirichlet forms Jürgen Jost ... Providence, RI American Math. Soc. [u.a.] 1998 XIV, 277 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: AMS, IP studies in advanced mathematics 8 Dirichlet-vormen gtt Probabilités ram Dirichlet forms Dirichletsche Form (DE-588)4150137-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1997 Anogeia gnd-content Dirichletsche Form (DE-588)4150137-8 s DE-604 Jost, Jürgen 1956- Sonstige (DE-588)115774564 oth American Mathematical Society: AMS, IP studies in advanced mathematics 8 (DE-604)BV011103148 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009116823&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | New directions in Dirichlet forms American Mathematical Society: AMS, IP studies in advanced mathematics Dirichlet-vormen gtt Probabilités ram Dirichlet forms Dirichletsche Form (DE-588)4150137-8 gnd |
| subject_GND | (DE-588)4150137-8 (DE-588)1071861417 |
| title | New directions in Dirichlet forms |
| title_auth | New directions in Dirichlet forms |
| title_exact_search | New directions in Dirichlet forms |
| title_full | New directions in Dirichlet forms Jürgen Jost ... |
| title_fullStr | New directions in Dirichlet forms Jürgen Jost ... |
| title_full_unstemmed | New directions in Dirichlet forms Jürgen Jost ... |
| title_short | New directions in Dirichlet forms |
| title_sort | new directions in dirichlet forms |
| topic | Dirichlet-vormen gtt Probabilités ram Dirichlet forms Dirichletsche Form (DE-588)4150137-8 gnd |
| topic_facet | Dirichlet-vormen Probabilités Dirichlet forms Dirichletsche Form Konferenzschrift 1997 Anogeia |
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