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Stochastic Analysis

  • Book
  • © 1997

Overview

Authors:
  1. Paul Malliavin

    1. Paris, France

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 313)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XI
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  2. Differential Calculus on Gaussian Probability Spaces

    1. Front Matter

      Pages 1-2
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    2. Gaussian Probability Spaces

      • Paul Malliavin
      Pages 3-27

    3. Gross-Stroock Sobolev Spaces over a Gaussian Probability Space

      • Paul Malliavin
      Pages 29-62

    4. Smoothness of Laws

      • Paul Malliavin
      Pages 63-83

  4. Stochastic Integrals

    1. Front Matter

      Pages 147-148
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    2. White Noise Stochastic Integrals as Divergences

      • Paul Malliavin
      Pages 149-171

    3. Itô’s Theory of Stochastic Integration

      • Paul Malliavin
      Pages 173-198

  5. Stochastic Differential Equations

    1. Front Matter

      Pages 201-202
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    2. From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle

      • Paul Malliavin
      Pages 203-235

    3. Elliptic Estimates Through Stochastic Analysis

      • Paul Malliavin
      Pages 237-251

  6. Stochastic Analysis in Infinite Dimensions

    1. Front Matter

      Pages 257-258
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    2. Stochastic Analysis on Wiener Spaces

      • Paul Malliavin
      Pages 259-271

    3. Path Spaces and Their Tangent Spaces

      • Paul Malliavin
      Pages 273-298

  7. Back Matter

    Pages 301-346
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Keywords

About this book

This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.

Authors and Affiliations

  • Paris, France

    Paul Malliavin

Bibliographic Information

  • Book Title: Stochastic Analysis

  • Authors: Paul Malliavin

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-15074-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Hardcover ISBN: 978-3-540-57024-0Published: 16 April 1997

  • eBook ISBN: 978-3-642-15074-6Published: 12 June 2015

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 347

  • Topics: Probability Theory and Stochastic Processes

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