Probability in Banach Spaces

Michel Ledoux, Michel Talagrand

492 pages, parution le 31/12/2002

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Résumé

New isoperimetric inequalities and random process techniques have recently appeared at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (e.g. boundedness and continuity of random processes, integrability and limit theorems for vector valued random variables) and of some of their links to Geometry of Banach spaces. Its purpose is to present some of the main aspects of this theory, from the foundations to the latest developments, treated with the most recent and updated tools. In particular, the most important features are the systematic use of isoperimetry and related concentration of measure phenomena (to study integrability and limit theorems for vector valued random variables), and recent abstract random process techniques (entropy and majorizing measures). Some examples of these probabilistic ideas to classical Banach space theory complete this exposition.

Contents

o- Isoperimetric Background and Generalities

Isoperimetric Inequalities and the Concentration of Measure Phenomenon
Generalities on Banach Space Valued Random Variables and Random Processes

1- Banach Space Valued Random Variables and Their Strong Limiting Properties

Gaussian Random Variables
Rademacher Averages
Stable Random Variables
Sums of Independent Random Variables
The Strong Law of Large Numbers
The Law of the Iterated Logarithm

2- Tightness of Vector Valued Random Variables and Regularity of Random Processes

Type and Cotype of Banach Spaces
The Central Limit Theorem
Regularity of Random Processes
Regularity of Gaussian and Stable Processes
Stationary Processes and Random Fourier Series
Empirical Process Methods in Probability in Banach Spaces
Applications to Banach Space Theory

L'auteur - Michel Ledoux

Ledoux, M., Universite Paul Sabatier, Toulouse, France;

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L'auteur - Michel Talagrand

University of Paris, France, and The Ohio State University

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michel Ledoux, Michel Talagrand
Parution	31/12/2002
Nb. de pages	492
Format	16,7 x 24,7
Couverture	Relié
Poids	1011g
Intérieur	Noir et Blanc
EAN13	9783540520139