Dirichlet forms and symmetric Markov processes:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York
De Gruyter
1994
|
| Series: | De Gruyter studies in mathematics
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis S. 369 - 388 |
| Physical Description: | viii, 392 Seiten |
| ISBN: | 311011626X |
Staff View
MARC
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| 264 | 1 | |a Berlin ; New York |b De Gruyter |c 1994 | |
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Record in the Search Index
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| adam_text | Contents
Preface v
Notation ix
Part I. Dirichlet forms
Chapter 1. Basic theory of Dirichlet forms 3
1.1. Basic notions 3
1.2. Examples 6
1.3. Closed forms and semigroups 15
1.4. Dirichlet forms and Markovian semigroups 23
1.5. Transience of Dirichlet spaces and extended Dirichlet spaces 32
1.6. Global properties of Markovian semigroups 46
Chapter 2. Potential theory for Dirichlet forms 64
2.1. Capacity and quasi continuity 64
2.2. Measures of finite energy integrals 74
2.3. Reduced functions and spectral synthesis 92
Chapter 3. The scope of Dirichlet forms 98
3.1. Closability and the smallest closed extensions 98
3.2. Formulae of Beurling Deny and LeJan 108
3.3. Maximum Markovian extensions 117
Part II. Symmetric Markov processes
Chapter 4. Analysis by symmetric Hunt processes 133
4.1. Smallness of sets and symmetry 134
4.2. Identification of potential theoretic notions 141
4.3. Orthogonal projections and hitting distributions 148
4.4. Parts of forms and processes 152
4.5. Continuity, killing and jumps of sample paths 158
4.6. Quasi notions, fine notions and global properties 167
viii Contents
Chapter 5. Stochastic analysis by additive functionate 180
5.1. Positive continuous additive functionals and smooth measures 180
5.2. Decomposition of additive functionals of finite energy 199
5.3. Martingale additive functionals and Beurling Deny formulae 212
5.4. Continuous additive functionals of zero energy 217
5.5. Extensions to additive functionals locally of finite energy 225
5.6. Martingale additive functionals of finite energy and stochastic
integrals 239
5.7. Forward and backward martingale additive functionals 248
Chapter 6. Transformations of forms and processes 258
6.1. Perturbed Dirichlet forms and killing by additive functionals 258
6.2. Traces of Dirichlet forms and time changes by additive functionals 265
6.3. Transformations by supermartingale multiplicative functionals 280
Chapter 7. Construction of symmetric Markov processes 292
7.1. Construction of a Markovian transition function 292
7.2. Construction of a symmetric Hunt process 296
7.3. Dirichlet forms and Hunt processes on a Lusin space 303
A Appendix 308
A. 1 Choquet capacities 308
A.2 An introduction to Hunt processes 310
A.3 A summary on martingale additive functionals 331
A.4 Regular representations of Dirichlet spaces 344
Notes 361
Bibliography 369
Index 389
|
| any_adam_object | 1 |
| author | Fukushima, Masatoshi 1935- Ōshima, Yōichi Takeda, Masayoshi |
| author_GND | (DE-588)110160827 (DE-588)114266425 (DE-588)114266441 |
| author_facet | Fukushima, Masatoshi 1935- Ōshima, Yōichi Takeda, Masayoshi |
| author_role | aut aut aut |
| author_sort | Fukushima, Masatoshi 1935- |
| author_variant | m f mf y ō yō m t mt |
| building | Verbundindex |
| bvnumber | BV009749593 |
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| classification_tum | MAT 607f MAT 103f |
| ctrlnum | (OCoLC)844835262 (DE-599)BVBBV009749593 |
| dewey-full | 519.23322 519.233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23322 519.233 |
| dewey-search | 519.23322 519.233 |
| dewey-sort | 3519.23322 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009749593 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:40:14Z |
| institution | BVB |
| isbn | 311011626X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006449129 |
| oclc_num | 844835262 |
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| physical | viii, 392 Seiten |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Fukushima, Masatoshi 1935- (DE-588)110160827 aut Dirichlet forms and symmetric Markov processes Masatoshi Fukushima ; Yōichi Ōshima ; Masayoshi Takeda Berlin ; New York De Gruyter 1994 viii, 392 Seiten txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 19 Literaturverzeichnis S. 369 - 388 Dirichletsche Form (DE-588)4150137-8 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Dirichletsche Form (DE-588)4150137-8 s Markov-Prozess (DE-588)4134948-9 s DE-604 Ōshima, Yōichi (DE-588)114266425 aut Takeda, Masayoshi (DE-588)114266441 aut Erscheint auch als Online-Ausgabe 978-3-11-088974-1 De Gruyter studies in mathematics 19 (DE-604)BV000005407 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006449129&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fukushima, Masatoshi 1935- Ōshima, Yōichi Takeda, Masayoshi Dirichlet forms and symmetric Markov processes De Gruyter studies in mathematics Dirichletsche Form (DE-588)4150137-8 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| subject_GND | (DE-588)4150137-8 (DE-588)4134948-9 |
| title | Dirichlet forms and symmetric Markov processes |
| title_auth | Dirichlet forms and symmetric Markov processes |
| title_exact_search | Dirichlet forms and symmetric Markov processes |
| title_full | Dirichlet forms and symmetric Markov processes Masatoshi Fukushima ; Yōichi Ōshima ; Masayoshi Takeda |
| title_fullStr | Dirichlet forms and symmetric Markov processes Masatoshi Fukushima ; Yōichi Ōshima ; Masayoshi Takeda |
| title_full_unstemmed | Dirichlet forms and symmetric Markov processes Masatoshi Fukushima ; Yōichi Ōshima ; Masayoshi Takeda |
| title_short | Dirichlet forms and symmetric Markov processes |
| title_sort | dirichlet forms and symmetric markov processes |
| topic | Dirichletsche Form (DE-588)4150137-8 gnd Markov-Prozess (DE-588)4134948-9 gnd |
| topic_facet | Dirichletsche Form Markov-Prozess |
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