## Probability Surveys

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

#### 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.

#### Article information

Source
Probab. Surveys, Volume 3 (2006), 170-205.

Dates
First available in Project Euclid: 5 May 2006

https://projecteuclid.org/euclid.ps/1146832695

Digital Object Identifier
doi:10.1214/154957806000000069

Mathematical Reviews number (MathSciNet)
MR2216965

Zentralblatt MATH identifier
1189.60110

#### Citation

Feyel, D.; Üstünel, A. S.; Zakai, M. The realization of positive random variables via absolutely continuous transformations of measure on Wiener space. Probab. Surveys 3 (2006), 170--205. doi:10.1214/154957806000000069. https://projecteuclid.org/euclid.ps/1146832695