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An introduction to analysis on Wiener space / Ali Süleyman Ustünel.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1610.Publication details: Berlin ; New York : Springer, ©1995.Description: 1 online resource (x, 93 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540446620
  • 3540446621
Subject(s): Additional physical formats: Print version:: Introduction to analysis on Wiener space.DDC classification:
  • 510 s 519.2 20
LOC classification:
  • QA3 .L28 no. 1610 QA274.2
Other classification:
  • 31.70
Online resources:
Contents:
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.
Summary: 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!
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

Includes bibliographical references (pages 91-93) and index.

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!

Print version record.

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.

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