Stochastic Analysis
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 stoch...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1997, 1997
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| Edition: | 1st ed. 1997 |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
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. 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