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 Probability Surveys > Vol. 3 (2006) open journal systems 

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

D. Feyel
A.S. Ustunel
M. Zakai, Technion - Israel Institute of Technology

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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Feyel, D., Ustunel, A.S., Zakai, M., The realization of positive random variables via absolutely continuous transformations of measure on Wiener space, Probability Surveys, 3, (2006), 170-205 (electronic).


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