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Probability in Banach Spaces
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Probability in Banach Spaces

Probability in Banach Spaces

Michel Ledoux, Michel Talagrand

492 pages, parution le 31/12/2002

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;

Autres livres de Michel Ledoux

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

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