Probability in Banach spaces: isoperimetry and processes
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
|
| Edition: | repr. of the 1991 ed. |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XII, 480 S. graph. Darst. |
| ISBN: | 9783642202117 |
Staff View
MARC
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| 245 | 1 | 0 | |a Probability in Banach spaces |b isoperimetry and processes |c Michel Ledoux ; Michel Talagrand |
| 250 | |a repr. of the 1991 ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XII, 480 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804148350087331840 |
|---|---|
| adam_text | Table
of Contents
Introduction
.................................................. 1
Notation
..................................................... 7
Part
0.
Isoperimetric Background and Generalities
Chapter
1.
Isoperimetric Inequalities and the Concentration
of Measure Phenomenon
....................................... 14
1.1
Some Isoperimetric Inequalities on the Sphere, in Gauss Space
and on the Cube
.......................................... 15
1.2
An Isoperimetric Inequality for Product Measures
............. 25
1.3
Martingale Inequalities
..................................... 30
Notes and References
.......................................... 34
Chapter
2.
Generalities on Banach Space Valued Random Variables
and Random Processes
........................................ 37
2.1
Banach Space Valued Radon Random Variables
............... 37
2.2
Random Processes and Vector Valued Random Variables
....... 43
2.3
Symmetric Random Variables and Levy s Inequalities
.......... 47
2.4
Some Inequalities for Real Valued Random Variables
........... 50
Notes and References
.......................................... 52
Part I. Banach Space Valued Random Variables
and Their Strong Limiting Properties
Chapter
3.
Gaussian Random Variables
.......................... 54
3.1
Integrability and Tail Behavior
.............................. 56
3.2
Integrability of Gaussian Chaos
............................. 64
3.3
Comparison Theorems
..................................... 73
Notes and References
.......................................... 87
X Table of Contents
Chapter
4.
Rademacher Averages
............................... 89
4.1
Real Rademacher Averages
................................. 89
4.2
The Contraction Principle
.................................. 95
4.3
Integrability and Tail Behavior of Rademacher Series
.......... 98
4.4
Integrability of Rademacher Chaos
.......................... 104
4.5
Comparison Theorems
.....................................
Ill
Notes and References
.......................................... 120
Chapter
5.
Stable Random Variables
............................ 122
5.1
Representation of Stable Random Variables
................... 124
5.2
Integrability and Tail Behavior
.............................. 133
5.3
Comparison Theorems
..................................... 141
Notes and References
.......................................... 147
Chapter
6.
Sums of Independent Random Variables
............... 149
6.1
Symmetrization and Some Inequalities for Sums of
Independent Random Variables
............................. 150
6.2
Integrability of Sums of Independent Random Variables
........ 155
6.3
Concentration and Tail Behavior
............................ 162
Notes and References
.......................................... 176
Chapter
7.
The Strong Law of Large Numbers
.................... 178
7.1
A General Statement for Strong Limit Theorems
.............. 179
7.2
Examples of Laws of Large Numbers
......................... 186
Notes and References
.......................................... 195
Chapter
8.
The Law of the Iterated Logarithm
.................... 196
8.1
Kolmogorov s Law of the Iterated Logarithm
.................. 196
8.2 Hartman-
Wintner-Strassen s Law of the Iterated Logarithm
.... 203
8.3
On the Identification of the Limits
........................... 216
Notes and References
.......................................... 233
Part II. Tightness of Vector Valued Random Variables
and Regularity of Random Processes
Chapter
9.
Type and Cotype of Banach Spaces
................... 236
9.1
¿p-Subspaces of Banach Spaces
.............................. 237
9.2
Type and Cotype
.......................................... 245
9.3
Some Probabilistic Statements in Presence
of Type and Cotype
....................................... 254
Notes and References
.......................................... 269
Table
of
Contents
XI
Chapter
10.
The Central Limit Theorem
......................... 272
10.1
Some General Facts About the Central Limit Theorem
........ 273
10.2
Some Central Limit Theorems in Certain
Danach
Spaces
...... 280
10.3
A Small Ball Criterion for the Central Limit Theorem
......... 289
Notes and References
.......................................... 295
Chapter
11.
Regularity of Random Processes
..................... 297
11.1
Regularity of Random Processes Under Metric
Entropy Conditions
....................................... 299
11.2
Regularity of Random Processes Under Majorizing
Measure Conditions
....................................... 309
11.3
Examples of Applications
.................................. 318
Notes and References
.......................................... 329
Chapter
12.
Regularity of Gaussian and Stable Processes
........... 332
12.1
Regularity of Gaussian Processes
........................... 333
12.2
Necessary Conditions for the Boundedness and
Continuity of Stable Processes
............................. 349
12.3
Applications and Conjectures on Rademacher Processes
....... 357
Notes and References
.......................................... 363
Chapter
13.
Stationary Processes and Random Fourier Series
....... 365
13.1
Stationarity and Entropy
.................................. 365
13.2
Random Fourier Series
.................................... 369
13.3
Stable Random Fourier Series and
Strongly Stationary Processes
.............................. 382
13.4
Vector Valued Random Fourier Series
....................... 387
Notes and References
.......................................... 392
Chapter
14.
Empirical Process Methods in Probability
in Banach Spaces
............................................. 394
14.1
The Central Limit Theorem for Lipschitz Processes
........... 395
14.2
Empirical Processes and Random Geometry
................. 402
14.3
Vapnik-Chervonenkis Classes of Sets
........................ 411
Notes and References
.......................................... 419
Chapter
15.
Applications to Banach Space Theory
................ 421
15.1
Subspaces of Small Codimension
........................... 421
15.2
Conjectures on Sudakov s
Minoration
for Chaos
.............. 427
15.3
An Inequality of J. Bourgain
............................... 430
15.4
Invertibility of
Submatrices
................................ 434
XII Table of
Contents
15.5
Embedding
Subspaces
of Lp into
i^ ........................
438
15.6
Majorizing
Measures on Ellipsoids
.......................... 448
15.7
Cotype of the Canonical Injection i^
—*■ ¿2,1 ................ 453
15.8
Miscellaneous Problems
................................... 456
Notes and References
.......................................... 459
References
................................................... 461
Subject Index
................................................ 478
Classics in Mathematics
Springer·Verlag
began publishing books in higher mathematics in
1920,
when the
series
Grundleken
der mathematischen Wissenschaften,
initially conceived as a
series of advanced textbooks, was founded by Richard
Courant. A
few years later,
a new series
Ergebnisse der Mathematik und ihrer Grenzgebiete,
survey reports of
recent mathematical research, was added. Of over
400
books published in these
series, many have become recognized classics and remain standard references for
their subject. Springer is reissuing a selected few of these highly successful books
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máe
them easily accessible to younger
generations of students and researchers
|
| any_adam_object | 1 |
| author | Ledoux, Michel 1958- Talagrand, Michel 1952- |
| author_GND | (DE-588)112924360 (DE-588)112924379 |
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| author_role | aut aut |
| author_sort | Ledoux, Michel 1958- |
| author_variant | m l ml m t mt |
| building | Verbundindex |
| bvnumber | BV039535912 |
| classification_rvk | SK 800 SK 820 |
| ctrlnum | (OCoLC)759529844 (DE-599)BVBBV039535912 |
| 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 |
| edition | repr. of the 1991 ed. |
| format | Book |
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| isbn | 9783642202117 |
| language | English |
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| physical | XII, 480 S. graph. Darst. |
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| series2 | Classics in mathematics |
| spelling | Ledoux, Michel 1958- Verfasser (DE-588)112924360 aut Probability in Banach spaces isoperimetry and processes Michel Ledoux ; Michel Talagrand repr. of the 1991 ed. Berlin [u.a.] Springer 2011 XII, 480 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Banach-Raum (DE-588)4004402-6 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Talagrand, Michel 1952- Verfasser (DE-588)112924379 aut Erscheint auch als Online-Ausgabe 978-3-642-20212-4 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024388097&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024388097&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Ledoux, Michel 1958- Talagrand, Michel 1952- Probability in Banach spaces isoperimetry and processes Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Banach-Raum (DE-588)4004402-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4004402-6 (DE-588)4064324-4 |
| title | Probability in Banach spaces isoperimetry and processes |
| title_auth | Probability in Banach spaces isoperimetry and processes |
| title_exact_search | Probability in Banach spaces isoperimetry and processes |
| title_full | Probability in Banach spaces isoperimetry and processes Michel Ledoux ; Michel Talagrand |
| title_fullStr | Probability in Banach spaces isoperimetry and processes Michel Ledoux ; Michel Talagrand |
| title_full_unstemmed | Probability in Banach spaces isoperimetry and processes Michel Ledoux ; Michel Talagrand |
| title_short | Probability in Banach spaces |
| title_sort | probability in banach spaces isoperimetry and processes |
| title_sub | isoperimetry and processes |
| topic | Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Banach-Raum (DE-588)4004402-6 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Banach-Raum Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024388097&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024388097&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ledouxmichel probabilityinbanachspacesisoperimetryandprocesses AT talagrandmichel probabilityinbanachspacesisoperimetryandprocesses |