Stochastic Analysis (Hardcover, 1997. Corr. 2nd)

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.