巴拿赫空间中的概率论 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

巴拿赫空间中的概率论 英文PDF格式电子书版下载

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Introduction1

Notation7

Part O.Isoperimetric Background and Generalities14

Chapter 1.Isoperimetric Inequalities and the Concentration of Measure Phenomenon14

1.1 Some Isoperimetric Inequalities on the Sphere,in Gauss Space and on the Cube15

1.2 An Isoperimetric Inequality for Product Measures25

1.3 Martingale Inequalities30

Notes and References34

Chapter 2.Generalities on Banach Space Valued Random Variables and Random Processes37

2.1 Banach Space Valued Radon Random Variables37

2.2 Random Processes and Vector Valued Random Variables43

2.3 Symmetric Random Variables and Lévy's Inequalities47

2.4 Some Inequalities for Real Valued Random Variables50

Notes and References52

Part Ⅰ.Banach Space Valued Random Variables and Their Strong Limiting Properties54

Chapter 3.Gaussian Random Variables54

3.1 Integrability and Tail Behavior56

3.2 Integrability of Gaussian Chaos64

3.3 Comparison Theorems73

Notes and References87

Chapter 4.Rademacher Averages89

4.1 Real Rademacher Averages89

4.2 The Contraction Principle95

4.3 Integrability and Tail Behavior of Rademacher Series98

4.4 Integrability of Rademacher Chaos104

4.5 Comparison Theorems111

Notes and References120

Chapter 5.Stable Random Variables122

5.1 Representation of Stable Random Variables124

5.2 Integrability and Tail Behavior133

5.3 Comparison Theorems141

Notes and References147

Chapter 6.Sums of Independent Random Variables149

6.1 Symmetrization and Some Inequalities for Sums of Independent Random Variables150

6.2 Integrability of Sums of Independent Random Variables155

6.3 Concentration and Tail Behavior162

Notes and References176

Chapter 7.The Strong Law of Large Numbers178

7.1 A General Statement for Strong Limit Theorems179

7.2 Examples of Laws of Large Numbers186

Notes and References195

Chapter 8.The Law of the Iterated Logarithm196

8.1 Kolmogorov's Law of the Iterated Logarithm196

8.2 Hartman-Wintner-Strassen's Law of the Iterated Logarithm203

8.3 On the Identification of the Limits216

Notes and References233

Part Ⅱ.Tightness of Vector Valued Random Variables and Regularity of Random Processes236

Chapter 9.Type and Cotype of Banach Spaces236

9.1 enp-Subspaces of Banach Spaces237

9.2 Type and Cotype245

9.3 Some Probabilistic Statements in Presence of Type and Cotype254

Notes and References269

Chapter 10.The Central Limit Theorem272

10.1 Some General Facts About the Central Limit Theorem273

10.2 Some Central Limit Theorems in Certain Banach Spaces280

10.3 A Small Ball Criterion for the Central Limit Theorem289

Notes and References295

Chapter 11.Regularity of Random Processes297

11.1 Regularity of Random Processes Under Metric Entropy Conditions299

11.2 Regularity of Random Processes Under Majorizing Measure Conditions309

11.3 Examples of Applications318

Notes and References329

Chapter 12.Regularity of Gaussian and Stable Processes332

12.1 Regularity of Gaussian Processes333

12.2 Necessary Conditions for the Boundedness and Continuity of Stable Processes349

12.3 Applications and Conjectures on Rademacher Processes357

Notes and References363

Chapter 13.Stationary Processes and Random Fourier Series365

13.1 Stationarity and Entropy365

13.2 Random Fourier Series369

13.3 Stable Random Fourier Series and Strongly Stationary Processes382

13.4 Vector Valued Random Fourier Series387

Notes and References392

Chapter 14.Empirical Process Methods in Probability in Banach Spaces394

14.1 The Central Limit Theorem for Lipschitz Processes395

14.2 Empirical Processes and Random Geometry402

14.3 Vapnik-Chervonenkis Classes of Sets411

Notes and References419

Chapter 15.Applications to Banach Space Theory421

15.1 Subspaces of Small Codimension421

15.2 Conjectures on Sudakov's Minoration for Chaos427

15.3 An Inequality of J.Bourgain430

15.4 Invertibility of Submatrices434

15.5 Embedding Subspaces of Lp into eNP438

15.6 Majorizing Measures on Ellipsoids448

15.7 Cotype of the Canonical Injectione eN∞→L2,1453

15.8 Miscellaneous Problems456

Notes and References459

References461

Subject Index478