An Introduction to Analysis on Wiener Space

Ali S. Üstünel

ISBN 10: 3540601708 / ISBN 13: 9783540601708

Editore: Springer Berlin Heidelberg, 1995

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Druck auf Anfrage Neuware - Printed after ordering - 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!

Codice articolo 9783540601708

Dati bibliografici

• Titolo: An Introduction to Analysis on Wiener Space
• Editore: Springer Berlin Heidelberg
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 3540601708
• ISBN 13: 9783540601708
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 7 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 7 millimetri di profondità
• Peso: 189 grammi

Descrizione articolo

Riassunto

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!

Contenuti

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.