Stochastic Analysis
Published on 30. April 1998
Book
Paperback/Softback
XII, 347 pages
978-3-642-15073-9 (ISBN)
Description
In 5 independent sections, this book accounts 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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1997
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Illustrations
XII, 347 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
651 gr
ISBN-13
978-3-642-15073-9 (9783642150739)
DOI
10.1007/978-3-642-15074-6
Schweitzer Classification
Other editions
Additional editions
Previous edition
Content
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. Stochastic Integrals.- Ch. 6 White Noise Stochastic Integrals as Divergence.- Ch. 7 Ito's Theory of Stochastic Integration.- Part IV. Stochastic Differential Equations.- Ch. 8 From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle.- Ch. 9 Elliptic Estimates through Stochastic Analysis.- Part V. Stochastic Analysis in Infinite Dimensions.- Ch. 10 Stochastic Analysis on Wiener Spaces.- Ch. 11 Path Spaces and their Tangent Spaces.- Index.- Bibliography.