An Introduction to Analysis on Wiener Space

Ali Süleyman Üstünel (auth.)9783540601708, 3-540-60170-8

This book gives the basis of the probabilistic functional analysis on Wiener space, developed during the last decade. The subject has progressed considerably in recent years thr- ough its links with QFT and the impact of Stochastic Calcu- lus of Variations of P. Malliavin. Although the latter deals essentially with the regularity of the laws of random varia- bles defined on the Wiener space, the book focuses on quite different subjects, i.e. independence, Ramer’s theorem, etc. First year graduate level in functional analysis and theory of stochastic processes is required (stochastic integration with respect to Brownian motion, Ito formula etc). It can be taught as a 1-semester course as it is, or in 2 semesters adding preliminaries from the theory of stochastic processes It is a user-friendly introduction to Malliavin calculus!

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Table of contents :
Preliminaries….Pages 1-7
Gross-Sobolev derivative, divergence and Ornstein-Uhlenbeck operator….Pages 9-18
Meyer inequalities….Pages 19-25
Hypercontractivity….Pages 27-30
L p -multipliers theorem, meyer inequalities and distributions….Pages 31-39
Some applications of the distributions….Pages 41-51
Positive distributions and applications….Pages 53-60
Characterization of independence of some Wiener functionals….Pages 61-67
Moment inequalities for Wiener functional….Pages 69-79
Introduction to the theorem of Ramer….Pages 81-90