Transformation of Measure on Wiener Space

16This 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. Basic probability theory and the Ito calculus are assumed known; the necessary results from the Malliavin calculus are presented in the appendix. Aimed at graduatestudents and researchers, it can be used as a text for a course or a seminar.04Some general results on transformation of measure.- Transformations on Wiener space induced by adapted shifts.- Transformation of measures induced by non-adapted shifts.- The Sard inequality on Wiener space.- Transformation of measure induced by anticipative flows and those induced by monotone shifts.- Generalized Radon-Nikodym derivatives.- Random rotations.- Degree theory on Wiener space and its application to transformation of measure.- Appendix: mainly dedicated to the Malliavin calculus and functional analysis on Wiener space.