Gaussian Hilbert spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
129 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 340 S. |
| ISBN: | 0521561280 9780521057202 |
Internformat
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| 245 | 1 | 0 | |a Gaussian Hilbert spaces |c Svante Janson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1997 | |
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Datensatz im Suchindex
| _version_ | 1804126169290768384 |
|---|---|
| adam_text | Contents
Introduction v11
Chapter 1. Gaussian spaces 1
1. Preliminaries 1
2. Gaussian random variables 3
3. Gaussian Hilbert spaces 4
4. Complex Gaussian spaces 12
5. Feynman diagrams 15
Chapter 2. Wiener chaos 17
Chapter 3. Wick products 23
1. Wick products of Gaussian variables 24
2. Wick exponentials 32
3. General Wick products 35
Chapter 4. Tensor products and Fock space 42
1. Spaces 42
2. Operators 45
3. Absolute continuity 53
Chapter 5. Hypercontractivity 57
1. Real hypercontractivity 57
2. Complex hypercontractivity 67
3. Multipliers 72
Chapter 6. Variables with finite chaos decompositions 78
Chapter 7. Stochastic integration 86
1. Brownian motion and ltd integrals 86
2. Stochastic integrals on general measure spaces 95
3. Skorohod integrals 105
4. Complex Gaussian stochastic measures 110
Chapter 8. Gaussian stochastic processes 117
1. The covariance function 117
2. The pseudometric 119
3. Continuity 120
4. The Cameron Martin space 120
Chapter 9. Conditioning 127
1. Introduction
2. Conditional expectations 128
3. Conditional distributions 132
4. Example: Random potential in a network 133
v
vi CONTENTS
Chapter 10. Pairs of Gaussian subspaces 142
1. Projections and singular numbers 142
2. Measures of dependence 143
Chapter 11. Limit theorems for generalized [/ statistics 150
1. )7 statistics 150
2. Asymmetric statistics 157
3. Random graphs 165
Chapter 12. Applications to operator theory 184
Chapter 13. Some operators from quantum physics 197
1. The Fourier Wiener transform 197
2. Annihilation and creation operators 200
3. Position and momentum operators 210
Chapter 14. The Cameron Martin shift 216
1. The Cameron Martin shift 216
2. Shifts and the Cameron Martin space 223
Chapter 15. Malliavin calculus 228
1. The directional derivative 229
2. The gradient operator 236
3. Higher derivatives 239
4. Absolute continuity 240
5. Sobolev spaces 245
6. The L2 case 257
7. Dense subspaces 261
8. The Meyer inequalities 266
9. The divergence operator 274
10. Smoothness 281
11. A new look at the Skorohod integral 283
Chapter 16. Transforms 286
1. The T and S transforms 286
2. More general Wick products 293
3. Fock space operators 298
4. Stochastic integration 300
5. The Cameron Martin shift 304
6. Malliavin calculus 304
Appendices 309
A. The monotone class theorem 309
B. Stochastic processes 311
C. Banach space valued functions and random variables 312
D. Polarization 314
E. Tensor products 315
F. Reproducing Hilbert Spaces 323
G. Analytic functions in Banach spaces 326
H. Hubert Schmidt operators and singular numbers 327
References 329
Index of notation 335
Index 337
|
| any_adam_object | 1 |
| author | Janson, Svante 1955- |
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| author_role | aut |
| author_sort | Janson, Svante 1955- |
| author_variant | s j sj |
| building | Verbundindex |
| bvnumber | BV011636827 |
| classification_rvk | SK 800 SK 820 |
| classification_tum | MAT 463f |
| ctrlnum | (OCoLC)246328270 (DE-599)BVBBV011636827 |
| dewey-full | 515.733 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.733 |
| dewey-search | 515.733 |
| dewey-sort | 3515.733 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:13:11Z |
| institution | BVB |
| isbn | 0521561280 9780521057202 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007842377 |
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| physical | X, 340 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
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| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Janson, Svante 1955- Verfasser (DE-588)139272658 aut Gaussian Hilbert spaces Svante Janson 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 X, 340 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 129 Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Normalverteilung (DE-588)4075494-7 gnd rswk-swf Normalverteilung (DE-588)4075494-7 s Hilbert-Raum (DE-588)4159850-7 s DE-604 Erscheint auch als Online-Ausgabe 978-0-511-52616-9 Cambridge tracts in mathematics 129 (DE-604)BV000000001 129 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007842377&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Janson, Svante 1955- Gaussian Hilbert spaces Cambridge tracts in mathematics Hilbert-Raum (DE-588)4159850-7 gnd Normalverteilung (DE-588)4075494-7 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4075494-7 |
| title | Gaussian Hilbert spaces |
| title_auth | Gaussian Hilbert spaces |
| title_exact_search | Gaussian Hilbert spaces |
| title_full | Gaussian Hilbert spaces Svante Janson |
| title_fullStr | Gaussian Hilbert spaces Svante Janson |
| title_full_unstemmed | Gaussian Hilbert spaces Svante Janson |
| title_short | Gaussian Hilbert spaces |
| title_sort | gaussian hilbert spaces |
| topic | Hilbert-Raum (DE-588)4159850-7 gnd Normalverteilung (DE-588)4075494-7 gnd |
| topic_facet | Hilbert-Raum Normalverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007842377&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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