TRANSFORMATION OF MESURE ON WIENER SPACE eBook

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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 transformations of measure induced by flows, the extensions 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.
INFORMATION

AUTEUR: A-Süleyman Ustunel

NOM DE FICHIER: TRANSFORMATION OF MESURE ON WIENER SPACE.pdf

DATE DE PUBLICATION: 1999-Dec-08

TAILLE DU FICHIER: 3,81 MB

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PDF Transformation of Measure on Wiener Space - GBV

Abstract: Let µ be a Gaussian measure on some measurable space {W = {w},B(W)} and let ν be a measure on the same space which is absolutely continuous with respect to ν. The paper surveys results on the problem of constructing a transformation T on the W space such that Tw = w+u(w) where u takes valuesinthe Cameron-Martinspace andthe image ...

Amazon.fr - Transformation of Measure on Wiener Space ...

students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of Paul Malliavin (cf. [55]). A portion of the material exposed is our own research, in particular, with Moshe Zakai and Denis Feyel for the rest we have used the works listed in the bibliography. The origin of this book goes back to ...

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