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2006 The realization of positive random variables via absolutely continuous transformations of measure on Wiener space
D. Feyel, A. S. Üstünel, M. Zakai
Probab. Surveys 3: 170-205 (2006). DOI: 10.1214/154957806000000069

Abstract

Let $\mu$ be a Gaussian measure on some measurable space $\{W = \{w\}, \mathcal{B}(W)\}$ and let $\nu$ be a measure on the same space which is absolutely continuous with respect to $\nu$. 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 values in the Cameron-Martin space and the image of $\mu$ under $T$ is $\mu$. In addition we ask for the existence of transformations $T$ belonging to some particular classes.

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D. Feyel. A. S. Üstünel. M. Zakai. "The realization of positive random variables via absolutely continuous transformations of measure on Wiener space." Probab. Surveys 3 170 - 205, 2006. https://doi.org/10.1214/154957806000000069

Information

Published: 2006
First available in Project Euclid: 5 May 2006

zbMATH: 1189.60110
MathSciNet: MR2216965
Digital Object Identifier: 10.1214/154957806000000069

Rights: Copyright © 2006 The Institute of Mathematical Statistics and the Bernoulli Society

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