Upper and Lower Bounds for Stochastic Processes: Modern Methods and Classical Problems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2014
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
60 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XV, 626 S. |
| ISBN: | 9783642540745 |
Staff View
MARC
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CONTENTS
1. PHILOSOPHY AND OVERVIEW OF THE BOOK 1
1.1 UNDERLYING PHILOSOPHY 1
1.2 PECULIARITIES OF STYLE 1
1.3 WHAT THIS BOOK IS REALLY ABOUT 2
1.4 GAUSSIAN PROCESSES AND THE GENERIC CHAINING 3
1.5 RANDOM FOURIER SERIES AND TRIGONOMETRIC SUMS, I 5
1.6 MATCHING THEOREMS, I 6
1.7 BERNOULLI PROCESSES 7
1.8 TREES AND THE ART OF LOWER BOUNDS 7
1.9 RANDOM FOURIER SERIES AND TRIGONOMETRIC SUMS, II 8
1.10 PROCESSES RELATED TO GAUSSIAN PROCESSES 8
1.11 THEORY AND PRACTICE OF EMPIRICAL PROCESSES 9
1.12 PARTITION SCHEME FOR FAMILIES OF DISTANCES 9
1.13 INFINITELY DIVISIBLE PROCESSES 10
1.14 THE FUNDAMENTAL CONJECTURES 10
1.15 CONVERGENCE OF ORTHOGONAL SERIES; MAJORIZING MEASURES 10
1.16 MATCHING THEOREMS II: SHOR'S MATCHING THEOREM 11
1.17 THE ULTIMATE MATCHING CONJECTURE IN DIMENSION 3 11
1.18 APPLICATIONS TO BANACH SPACE THEORY 11
1.19 APPENDIX B: CONTINUITY 12
REFERENCE 12
2. GAUSSIAN PROCESSES AND THE GENERIC CHAINING 13
2.1 OVERVIEW 13
2.2 THE GENERIC CHAINING 13
2.3 FUNCTIONALS 32
2.4 GAUSSIAN PROCESSES AND THE MYSTERIES OF HILBERT SPACE 40
2.5 A FIRST LOOK AT ELLIPSOIDS 51
2.6 PROOF OF THE FUNDAMENTAL PARTITIONING THEOREM 55
2.7 A GENERAL PARTITIONING SCHEME 61
2.8 NOTES AND COMMENTS 70
REFERENCES 73
HTTP://D-NB.INFO/1045790192
75
75
77
86
88
89
91
91
100
106
115
125
127
129
129
131
141
146
149
152
161
170
170
173
173
173
180
183
192
197
199
199
200
203
206
212
221
227
231
232
CONTENTS
RANDOM FOURIER SERIES AND TRIGONOMETRIC SUMS, I.
3.1 TRANSLATION INVARIANT DISTANCES
3.2 THE MARCUS-PISIER THEOREM
3.3 A THEOREM OF FERNIQUE
3.4 NOTES AND COMMENTS
REFERENCES
MATCHING THEOREMS, I
4.1 THE ELLIPSOID THEOREM
4.2 MATCLIINGS
4.3 THE AJTAI, KOMLOS, TUSNADY MATCHING THEOREM .
4.4 THE LEIGHTON-SHOR GRID MATCHING THEOREM
4.5 NOTES AND COMMENTS
REFERENCES
BERNOULLI PROCESSES
5.1 BOUNDEDNESS OF BERNOULLI PROCESSES
5.2 CHAINING FOR BERNOULLI PROCESSES
5.3 FUNDAMENTAL TOOLS FOR BERNOULLI PROCESSES
5.4 CONTROL IN T NORM
5.5 LATALA'S PRINCIPLE
5.6 CHOPPING MAPS AND FUNCTIONALS
5.7 THE DECOMPOSITION LEMMA
5.8 NOTES AND COMMENTS
REFERENCES
TREES AND THE ART OF LOWER BOUNDS
6.1 INTRODUCTION
6.2 TREES
6.3 A TOY LOWER BOUND
6.4 LOWER BOUND FOR THEOREM 4.3.2
6.5 LOWER BOUND FOR THEOREM 4.4.1
REFERENCE
RANDOM FOURIER SERIES AND TRIGONOMETRIC SUMS, II
7.1 INTRODUCTION
7.2 FAMILIES OF DISTANCES
7.3 STATEMENT OF MAIN RESULTS
7.4 PROOFS, LOWER BOUNDS
7.5 PROOFS, UPPER BOUNDS
7.6 PROOFS, CONVERGENCE
7.7 EXPLICIT COMPUTATIONS
7.8 NOTES AND COMMENTS
REFERENCES
CONTENTS XIII
8. PROCESSES RELATED TO GAUSSIAN PROCESSES 233
8.1 P-STABLE PROCESSES 233
8.2 ORDER 2 GAUSSIAN CHAOS 243
8.3 TAILS OF MULTIPLE ORDER GAUSSIAN CHAOS 255
8.4 NOTES AND COMMENTS 269
REFERENCES 269
9. THEORY AND PRACTICE OF EMPIRICAL PROCESSES 271
9.1 DISCREPANCY BOUNDS 271
9.2 HOW TO APPROACH PRACTICAL PROBLEMS 282
9.3 THE CLASS OF SQUARES OF A GIVEN CLASS 283
9.4 WHEN NOT TO USE CHAINING 303
9.5 NOTES AND COMMENTS 310
REFERENCES 310
10. PARTITION SCHEME FOR FAMILIES OF DISTANCES 313
10.1 THE PARTITION SCHEME 313
10.2 THE STRUCTURE OF CERTAIN CANONICAL PROCESSES 318
REFERENCES 330
11. INFINITELY DIVISIBLE PROCESSES 331
11.1 A WEIL-KEPT SECRET 331
11.2 OVERVIEW OF RESULTS 332
11.3 ROSINSKI'S REPRESENTATION 344
11.4 THE HARMONIC CASE 348
11.5 PROOF OF THE DECOMPOSITION THEOREM 354
11.6 PROOF OF THE MAIN LOWER BOUND 358
REFERENCES 369
12. THE FUNDAMENTAL CONJECTURES 371
12.1 INTRODUCTION 371
12.2 SELECTOR PROCESSES 371
12.3 THE GENERALIZED BERNOULLI CONJECTURE 372
12.4 POSITIVE SELECTOR PROCESSES 384
12.5 EXPLICITLY SMALL EVENTS 386
12.6 CLASSES OF SETS 393
REFERENCES 398
13. CONVERGENCE OF ORTHOGONAL SERIES; MAJORIZING MEASURES . . 399
13.1 INTRODUCTION 399
13.2 CHAINING, I 408
13.3 PROOF OF BEDNORZ'S THEOREM 412
13.4 PERMUTATIONS 420
13.5 CHAINING, II 429
13.6 CHAINING, III 443
XIV CONTENTS
13.7 NOTES AND COMMENTS 444
REFERENCES 445
14. MATCHING THEOREMS, II: SHOR'S MATCHING THEOREM 447
1.4.1 INTRODUCTION 447
14.2 THE DISCREPANCY THEOREM 448
14.3 DECOMPOSITION OF FUNCTIONS OF
H
453
14.4 DISCRETE FOURIER TRANSFORM 461
14.5 MAIN ESTIMATES 464
14.6 PROOF OF PROPOSITION 14.2.4 472
14.7 NOTES AND COMMENTS 474
REFERENCES 474
15. THE ULTIMATE MATCHING THEOREM IN DIMENSION 3 475
15.1 INTRODUCTION 475
15.2 THE CRUCIAL DISCREPANCY BOUND 480
15.3 CLEANING UP IP 484
15.4 GEOMETRY 488
15.5 PROBABILITY, I 494
15.6 HAAR BASIS EXPANSION 500
15.7 PROBABILITY, II 506
REFERENCES 513
16. APPLICATIONS TO BANACH SPACE THEORY 515
16.1 COTYPE OF OPERATORS FROM C(K) 515
16.2 COMPUTING THE RADEMACHER COTYPE-2 CONSTANT 527
16.3 CLASSIFYING THE ELEMENTS OF B\ 533
16.4 1-UNCONDITIONAL BASES AND GAUSSIAN MEASURES 536
16.5 RESTRICTION OF OPERATORS 546
16.6 THE YL(P)-PROBLEM 554
16.7 PROPORTIONAL SUBSETS OF BOUNDED ORTHOGONAL SYSTEMS 561
16.8 EMBEDDING SUBSPACES OF L
P
INTO
PN
572
16.9 GORDON'S EMBEDDING THEOREM 588
16.10 NOTES AND COMMENTS 591
REFERENCES 592
A. APPENDIX: WHAT THIS BOOK IS REALLY ABOUT 595
A.L INTRODUCTION 595
A.2 THE KOLRNOGOROV CONDITIONS 595
A.3 MORE CHAINING IN R
M
597
A.4 THE GARSIA-RODEMICH-RURNSEY LEMMA 598
A.5 CHAINING IN A METRIC SPACE 599
A.6 TWO CLASSICAL INEQUALITIES 601
CONTENTS XV
B. APPENDIX: CONTINUITY 607
B.L INTRODUCTION 607
B.2 CONTINUITY UNDER METRIC ENTROPY CONDITIONS 607
B.3 CONTINUITY OF GAUSSIAN PROCESSES 613
REFERENCES 617
INDEX 625 |
| any_adam_object | 1 |
| author | Talagrand, Michel 1952- |
| author_GND | (DE-588)112924379 |
| author_facet | Talagrand, Michel 1952- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| series | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge |
| spelling | Talagrand, Michel 1952- Verfasser (DE-588)112924379 aut Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems Michel Talagrand Berlin Springer 2014 XV, 626 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 60 Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Untere Schranke (DE-588)4186970-9 gnd rswk-swf Obere Schranke (DE-588)4470960-2 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Obere Schranke (DE-588)4470960-2 s Untere Schranke (DE-588)4186970-9 s 1\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge 60 (DE-604)BV000899194 60 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4555703&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027173722&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Talagrand, Michel 1952- Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge Stochastischer Prozess (DE-588)4057630-9 gnd Untere Schranke (DE-588)4186970-9 gnd Obere Schranke (DE-588)4470960-2 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4186970-9 (DE-588)4470960-2 |
| title | Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems |
| title_auth | Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems |
| title_exact_search | Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems |
| title_full | Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems Michel Talagrand |
| title_fullStr | Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems Michel Talagrand |
| title_full_unstemmed | Upper and Lower Bounds for Stochastic Processes Modern Methods and Classical Problems Michel Talagrand |
| title_short | Upper and Lower Bounds for Stochastic Processes |
| title_sort | upper and lower bounds for stochastic processes modern methods and classical problems |
| title_sub | Modern Methods and Classical Problems |
| topic | Stochastischer Prozess (DE-588)4057630-9 gnd Untere Schranke (DE-588)4186970-9 gnd Obere Schranke (DE-588)4470960-2 gnd |
| topic_facet | Stochastischer Prozess Untere Schranke Obere Schranke |
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