Stochastic Analysis / Edition 1

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

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Product Details

  • ISBN-13: 9783540570240
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/31/1997
  • Series: Grundlehren der mathematischen Wissenschaften Series, #313
  • Edition description: 1st ed. 1997. 2nd printing 2002
  • Edition number: 1
  • Pages: 376
  • Product dimensions: 0.88 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Contents: Part I. Differential Calculus on Gaussian Probability Spaces.- Ch. 1 Gaussian probability spaces.- Ch. 2 Gross-Stroock Sobolev Spaces over a Gaussian Probability Space.- Ch. 3 Smoothness of Laws.- Part II. Quasi-Sure Analysis.- Ch. 4 Foundations of Quasi-Sure Analysis: Hierarchy of Capacities and Precise Gaussian Probability Space.- Ch. 5 Differential Geometry on a Precise Gaussian Probability Space.- Part III. Shastic Integrals.- Ch. 6 White Noise Shastic Integrals as Divergence.- Ch. 7 Ito's Theory of Shastic Integration.- Part IV. Shastic Differential Equations.- Ch. 8 From Ordinary Differential Equations to Shastic Flow: The Transfer Principle.- Ch. 9 Elliptic Estimates through Shastic Analysis.- Part V. Shastic Analysis in Infinite Dimensions.- Ch. 10 Shastic Analysis on Wiener Spaces.- Ch. 11 Path Spaces and their Tangent Spaces.- Index.- Bibliography.

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