The realization of positive random variables via absolutely continuous transformations of measure on Wiener space

Details The realization of positive random variables via absolutely continuous transformations of measure on Wiener space The realization of positive random variables via absolutely continuous transformations of measure on Wiener space

2005-11-22

arxiv.org/abs/math/0511545v2

Probability Surveys 2006, Vol. 3, 170-205

Mathematics

Probability

Published at http://dx.doi.org/10.1214/154957806000000069 in the Probability Surveys (http://www.i-journals.org/ps/) by the In

Scientific paper

10.1214/154957806000000069

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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