Economics/Finances Probability in Banach Spaces: Isoperimetry and Processes (3540520139)

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Probability in Banach Spaces: Isoperimetry and Processes

(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics): Michel Ledoux, Michel Talagrand

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.

Summary: A must in modern Probability Theory

Rating: 5

This book is the standard for all who seek detailed information about stochastics in Banach spaces. Written from two of the top researchers in this area, it provides a broad area of topics, a concise treatment of deep results and exhaustive references. Sadly enough, it is out of print now, but I hope for a 2nd edition.

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