Paul Malliavin

Stochastic Analysis

• Gebundenes Buch

Produktbeschreibung

This book, written by the founder of the stochastic calculus of variations, now a wide and prolific field of research, is divided into five independent parts that can each be read independently of the others. It is an account of the main recent developments in the field, taking care however over the geometric foundations, particularly the intrinsic point of view. Analytic applications are also presented. Included is the first presentation in book-form of quasi-sure analysis.
The book includes a vast bibliography of close to 800 items, and will be most valuable to all stochastic analysts. Parts of it can also be used for graduate courses.

Produktdetails

• Grundlehren der mathematischen Wissenschaften 313
• Verlag: Springer, Berlin
• 1st ed. 1997. Corr. 2nd printing 0
• Seitenzahl: 364
• Erscheinungstermin: 16. April 1997
• Englisch
• Abmessung: 241mm x 160mm x 26mm
• Gewicht: 664g
• ISBN-13: 9783540570240
• ISBN-10: 3540570241
• Artikelnr.: 06886136

Inhaltsangabe

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.