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: 4,69 MB

TÉLÉCHARGER LIRE EN LIGNE

[math/0511545] The realization of positive random ...

Of all measures in function spaces, we know most about Wiener measure especially because of a long series of papers by R. H. Cameron and W. T. Martin on the Wiener integral. One result, the linear transformation theorem [3], has recently been generalized but still for Wiener measure by one of Cameron's students, D. A. Woodward [13]. The purpose of our paper is to state and prove an analog of ...

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