This book tries to present some of the main aspects of the theory of Probability in Banach spaces， from the foundations of the topic to the latest developments and current research questions. The past twenty years saw intense activity in the study of classical Probability Theory on infinite dimensional spaces. vector valued random variables， boundedness and continuity of ran-dom processes， with a fruitful interaction with classical Banach spaces and their geometry. A large community of mathematicians， from classical probabilists to pure analysts and functional analysts， participated to this common achievement.The recent use of isoperimetric tools and concentration of measure phenomena， and of abstract random process techniques has led today to rather a complete picture of the field. These developments prompted the authors to undertake the writing of this exposition based on this modern point of view.This book does not pretend to cover all the aspects of the subject and of its connections with other fields. In spite of its ommissions， imperfections and errors， for which we would like to apologize， we hope that this work gives an attractive picture of the subject and will serve it appropriately.
作者簡介
暫缺《巴拿赫空間中的概率論》作者簡介
圖書目錄
Introduction Notation Part 0. Isoperimetric Background and Generalities Chapter 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon 1.1 ome Isoperimetric Inequalities on the Sphere, in Gauss Space and on the Cube 1.2 An Isoperimetric Inequality for Product Measures 1.3 Martingale Inequalities Notes and References Chapter 2. Generalities on Banach Space Valued Random Variables and Random Processes 2.1 Banach Space Valued Radon Random Variables 2.2 Random Processes and Vector Valued R,a,ndom Variables 2.3 Symmetric Random Variables and Levy's Inequalities 2.4 Some Inequalities for Real Valued Random Variables Notes and References Part I. Banach Space Valued Random Variables and Their Strong Limiting Properties Chapter 3. Gaussian Random Variables 3.1 Integrability and Tail Behavior 3.2 Integrability of Gaussian Chaos 3.3 Comparison Theorems Notes and References Chapter 4. Rademacher Averages 4.1 Real Rademacher A'verages 4.2 The Contraction Principle 4,3 Integrability and Tail Behavior of Rademacher Series 4.4 Integrability of Rademacher Chaos 4.5 Comparison Theorems Notes and References Chapter 5. Stable Random Variables 5.1 R;epresentation of Stable Random Variables 5.2 Integrability and Tail Behavior 5.3 Comparison Theorems Notes and References Chapter 6. Sums of Independent Random Variables 6.1 Symmetrization and Some Inequalities for Sums of Independent Random Variables 6.2 Integrability of Sums of Independent Random Variables 6.3 Concentration and Tail Behavior Notes and R,eferences Chapter 7. The Strong Law of Large Numbers 7.1 A General Statement for Strong Limit Theorems 7.2 Examples of Laws of Large Numbers Notes and References Chapter 8. The Law of the lterated Logarithm 8.1 Kolmogorov's Law of the Iterated Logarithm 8.2 Hartman-Wintner-Strassen's Law of the Iterated Logarithm 8.3 On the Identification of the Limits Notes and References Part II. Tightness of Vector Valued R,andom Variables and Regularity of Random Processes ……
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