发帖
雷达卡
Authors: Ali Süleyman üstünel, Moshe Zakai
This book gives a systematic presentation of the main results on the transformation of measure induced by shift transformations on Wiener space. This topic has its origins in the work of Cameron and Martin (anticipative shifts, 1940's) and that of Girsanov (non-anticipative shifts, 1960's). It played an important role in the development of non-anticipative stochastic calculus and itself developed under the impulse of the stochastic calculus of variations. The recent results presented in the book include a dimension-free form of the Girsanov theorem, the transformations of measure induced by anticipative non-invertible shift transformations, the transformation of measure induced by flows, the extension of the notions of Sard lemma and degree theory to Wiener space, generalized distribution valued Radon-Nikodym theorems and measure preserving transformations. Basic probability theory and the Ito calculus are assumed known; the necessary results from the Malliavin calculus are presented in the appendix. Aimed at graduate students and researchers, it can be used as a text for a course or a seminar.
Table of contents
Front Matter
Pages I-XIII
Introduction
Pages 1-4
Some Background Material and Preliminary Results
Pages 5-19
Transformation of Measure Induced by Adapted Shifts
Pages 21-51
Transformation of Measure Induced by General Shifts
Pages 53-98
The Sard Inequality
Pages 99-113
Transformation of Measure Under Anticipative Flows
Pages 115-156
Monotone Shifts
Pages 157-180
Generalized Radon-Nikodym Derivatives
Pages 181-205
Random Rotations
Pages 207-231
The Degree Theorem on Wiener Space
Pages 233-254
Back Matter
Pages 255-297
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