On the geometry of diffusion operators and stochastic flows:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1999
|
| Series: | Lecture notes in mathematics
1720 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 118 S. |
| ISBN: | 3540667083 |
Staff View
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| 245 | 1 | 0 | |a On the geometry of diffusion operators and stochastic flows |c K. D. Elworthy ; Y. Le Jan ; X.-M. Li |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
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| 490 | 1 | |a Lecture notes in mathematics |v 1720 | |
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Record in the Search Index
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| adam_text | Contents
Introduction 3
1 Construction of connections 7
1.1 Construction of connections 7
1.2 Basic Classes of Examples 14
1.3 Adjoint connections, torsion skew symmetry, basic formulae ... 18
1.4 Example: Homogeneous spaces continued 26
2 The infinitesimal generators and associated operators 30
2.1 The irrelevance of drift in dimension greater than 1 30
2.2 Torsion Skew Symmetry 35
2.3 The divergence operator 6 37
2.4 Hormander form generators on differential forms 42
2.5 On the infinitesimal generator 47
2.5.1 Example 47
2.5.2 Symmetricity of the generator Aq 49
3 Decomposition of noise and filtering 57
3.1 A canonical decomposition of the noise driving a stochastic dif¬
ferential equation 57
3.2 Canonical decomposition of the Gaussian field Wt 60
3.3 Filtering out redundant noise 63
3.3.1 When A does not belong to the image of X 69
3.3.2 The inverse derivative flow 72
3.3.3 Integrability of certain C norms for compact M 72
3.3.4 The semigroup on forms: Bochner type vanishing theorems 73
3.3.5 Bismut formulae 75
4 Application: Analysis on spaces of paths 76
4.1 Integration by parts and Clark Ocone formulae 78
4.2 Logarithmic Sobolev Inequality 82
4.3 Analysis on Cid(DiffM) 83
5 Stability of stochastic dynamical systems 87
2
6 Appendices 95
A Universal Connections as L W connection 95
B Creation and Annihilation operators (notation for section 2.4) . . 101
C Basic formulae 103
D List of notation 109
|
| any_adam_object | 1 |
| author | Elworthy, Kenneth David 1940- Le Jan, Yves 1952- Li, Xue-Mei 1964- |
| author_GND | (DE-588)114998132 (DE-588)121457400 (DE-588)121457397 |
| author_facet | Elworthy, Kenneth David 1940- Le Jan, Yves 1952- Li, Xue-Mei 1964- |
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| author_sort | Elworthy, Kenneth David 1940- |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)247860273 (DE-599)BVBBV012815264 |
| dewey-full | 510 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 519 - Probabilities and applied mathematics |
| dewey-raw | 510 519.23 |
| dewey-search | 510 519.23 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012815264 |
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| indexdate | 2024-07-09T18:34:10Z |
| institution | BVB |
| isbn | 3540667083 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008717329 |
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| physical | 118 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Elworthy, Kenneth David 1940- Verfasser (DE-588)114998132 aut On the geometry of diffusion operators and stochastic flows K. D. Elworthy ; Y. Le Jan ; X.-M. Li Berlin [u.a.] Springer 1999 118 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1720 Diffusionsprozess - Stochastischer Fluss - Stochastische Differentialgleichung - Differentialgeometrie Stochastische Analysis (DE-588)4132272-1 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Operator (DE-588)4130529-2 s Stochastische Analysis (DE-588)4132272-1 s DE-604 Le Jan, Yves 1952- Verfasser (DE-588)121457400 aut Li, Xue-Mei 1964- Verfasser (DE-588)121457397 aut Lecture notes in mathematics 1720 (DE-604)BV000676446 1720 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008717329&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elworthy, Kenneth David 1940- Le Jan, Yves 1952- Li, Xue-Mei 1964- On the geometry of diffusion operators and stochastic flows Lecture notes in mathematics Diffusionsprozess - Stochastischer Fluss - Stochastische Differentialgleichung - Differentialgeometrie Stochastische Analysis (DE-588)4132272-1 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4132272-1 (DE-588)4130529-2 (DE-588)4113937-9 |
| title | On the geometry of diffusion operators and stochastic flows |
| title_auth | On the geometry of diffusion operators and stochastic flows |
| title_exact_search | On the geometry of diffusion operators and stochastic flows |
| title_full | On the geometry of diffusion operators and stochastic flows K. D. Elworthy ; Y. Le Jan ; X.-M. Li |
| title_fullStr | On the geometry of diffusion operators and stochastic flows K. D. Elworthy ; Y. Le Jan ; X.-M. Li |
| title_full_unstemmed | On the geometry of diffusion operators and stochastic flows K. D. Elworthy ; Y. Le Jan ; X.-M. Li |
| title_short | On the geometry of diffusion operators and stochastic flows |
| title_sort | on the geometry of diffusion operators and stochastic flows |
| topic | Diffusionsprozess - Stochastischer Fluss - Stochastische Differentialgleichung - Differentialgeometrie Stochastische Analysis (DE-588)4132272-1 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Diffusionsprozess - Stochastischer Fluss - Stochastische Differentialgleichung - Differentialgeometrie Stochastische Analysis Operator Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008717329&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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