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 The realization of positive random variables via absolutely continuous transformations of measure on Wiener space
 D. FeyelA.S. UstunelM. Zakai, Technion - Israel Institute of Technology

 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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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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