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＜電子ブック＞
An Introduction to Analysis on Wiener Space / by Ali S. Üstünel
(Lecture Notes in Mathematics. ISSN:16179692 ; 1610)

版	1st ed. 1995.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1995
大きさ	X, 102 p : online resource
著者標目	*Üstünel, Ali S author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Probabilities LCSH:Mathematical physics FREE:Functional Analysis FREE:Probability Theory FREE:Theoretical, Mathematical and Computational Physics
一般注記	Preliminaries -- Gross-Sobolev derivative, divergence and Ornstein-Uhlenbeck operator -- Meyer inequalities -- Hypercontractivity -- L p -multipliers theorem, meyer inequalities and distributions -- Some applications of the distributions -- Positive distributions and applications -- Characterization of independence of some Wiener functionals -- Moment inequalities for Wiener functional -- to the theorem of Ramer 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! HTTP:URL=https://doi.org/10.1007/BFb0096328

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