Transformation of Measure on Wiener Space
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Beschreibung
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.
No other book on this subject Addresses fundamental problems and will be the standard reference for a long time to come The authors have different scientific origins and combine these successfully in the comined authorship of this book Includes supplementary material: sn.pub/extras
Autor*in
A.Süleyman Üstünel
Themen in »Transformation of Measure on Wiener Space«
Derivative Probability theory Stochastic calculus abstract Wiener space calculus functional analysis measure