Gaussian measures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1998]
|
| Series: | Mathematical surveys and monographs
Volume 62 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xii, 433 Seiten |
| ISBN: | 0821810545 9781470418694 |
Staff View
MARC
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| 100 | 1 | |a Bogačev, Vladimir I. |d 1961- |0 (DE-588)121192318 |4 aut | |
| 240 | 1 | 0 | |a Gaussovskie mery |
| 245 | 1 | 0 | |a Gaussian measures |c Vladimir I. Bogachev |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1998] | |
| 264 | 4 | |c © 1998 | |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 62 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Gaussian measures | |
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Record in the Search Index
| _version_ | 1819359449463128064 |
|---|---|
| adam_text | Contents
Preface
xi
Chapter
1.
Finite Dimensional Gaussian Distributions
1
1.1.
Gaussian measures on the real line
1
1.2.
Multivariate Gaussian distributions
3
1.3.
Hermite polynomials
7
1.4.
The Ornstein-Uhlenbeck semigroup
9
1.5.
Sobolev classes
12
1.6.
Hypercontractivity
16
1.7.
Several useful estimates
19
1.8.
Convexity inequalities
25
1.9.
Characterizations of Gaussian measures
30
1.10.
Complements and problems
33
Chapter
2.
Infinite Dimensional Gaussian Distributions
39
2.1.
Cylindrical sets
39
2.2.
Basic definitions
42
2.3.
Examples
48
2.4.
The Cameron-Martin space
59
2.5.
Zero-one laws
64
2.6.
Separability and oscillations
67
2.7.
Equivalence and singularity
71
2.8.
Measurable seminorms
74
2.9.
The Ornstein-Uhlenbeck semigroup
78
2.10.
Measurable linear functionals
79
2.11.
Stochastic integrals
83
2.12.
Complements and problems
90
Chapter
3.
Radon Gaussian Measures
97
3.1.
Radon measures
97
3.2.
Basic properties of Radon Gaussian measures
100
3.3.
Gaussian covariances
104
3.4.
The structure of Radon Gaussian measures
109
3.5.
Gaussian series
112
3.6.
Supports of Gaussian measures
119
3.7.
Measurable linear operators
122
3.8.
Weak convergence of Gaussian measures
129
3.9.
Abstract Wiener spaces
136
3.10.
Conditional measures and conditional expectations
140
3.11.
Complements and problems
142
Chapter
4.
Convexity of Gaussian Measures
157
4.1.
Gaussian symmetrization
157
4.2.
Ehrhard s inequality
162
4.3.
Isoperimetric inequalities
167
4.4.
Convex functions
171
4.5.
-řř-Lipschitzian
functions
174
4.6.
Correlation inequalities
177
4.7.
The Onsager-Machlup functions
181
4.8.
Small ball probabilities
187
4.9.
Large deviations
195
4.10.
Complements and problems
197
Chapter
5.
Sobolev Classes over Gaussian Measures
205
5.1.
Integration by parts
205
5.2.
The Sobolev classes Wp r and D^
211
5.3.
The Sobolev classes
Hp r
215
5.4.
Properties of Sobolev classes and examples
218
5.5.
The logarithmic Sobolev inequality
226
5.6.
Multipliers and Meyer s inequalities
229
5.7.
Equivalence of different definitions
234
5.8.
Divergence of vector fields
238
5.9.
Gaussian capacities
243
5.10.
Measurable polynomials
249
5.11.
Differentiability of
iï-Lipschitzian
functions
261
5.12.
Complements and problems
266
Chapter
6.
Nonlinear Transformations of Gaussian Measures
279
6.1.
Auxiliary results
279
6.2.
Measurable linear automorphisms
282
6.3.
Linear transformations
285
6.4.
Radon-Nikodym densities
288
6.5.
Examples of equivalent measures and linear transformations
295
6.6.
Nonlinear transformations
298
6.7.
Examples of nonlinear transformations
308
6.8.
Finite dimensional mappings
314
6.9.
Malliavin s method
316
6.10.
Surface measures
321
6.11.
Complements and problems
324
Chapter
7.
Applications
333
7.1.
Trajectories of Gaussian processes
333
7.2.
Infinite dimensional Wiener processes
336
7.3.
Logarithmic gradients
339
7.4.
Spherically symmetric measures
344
7.5.
Infinite dimensional diffusions
346
7.6.
Complements and problems
353
Appendix A. Locally Convex Spaces, Operators, and Measures
361
A.I. Locally convex spaces
361
A.
2.
Linear operators
365
A.3. Measures and measurability
371
Bibliographical Comments
381
References
391
Index
427
|
| any_adam_object | 1 |
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| author_facet | Bogačev, Vladimir I. 1961- |
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| classification_tum | MAT 603f |
| ctrlnum | (OCoLC)246127424 (DE-599)BVBBV012581820 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012581820 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:32:47Z |
| institution | BVB |
| isbn | 0821810545 9781470418694 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008544973 |
| oclc_num | 246127424 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-739 DE-29T DE-83 DE-384 DE-706 DE-11 DE-188 DE-20 |
| physical | xii, 433 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Bogačev, Vladimir I. 1961- Gaussian measures Mathematical surveys and monographs Gaussian measures Gauß-Maß (DE-588)4156113-2 gnd |
| subject_GND | (DE-588)4156113-2 |
| title | Gaussian measures |
| title_alt | Gaussovskie mery |
| title_auth | Gaussian measures |
| title_exact_search | Gaussian measures |
| title_full | Gaussian measures Vladimir I. Bogachev |
| title_fullStr | Gaussian measures Vladimir I. Bogachev |
| title_full_unstemmed | Gaussian measures Vladimir I. Bogachev |
| title_short | Gaussian measures |
| title_sort | gaussian measures |
| topic | Gaussian measures Gauß-Maß (DE-588)4156113-2 gnd |
| topic_facet | Gaussian measures Gauß-Maß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008544973&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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