正随机变量在Wiener空间上测度的absolutely continuous变换的实现
The realization of positive random variables via absolutely continuous transformations of measure on Wiener space
摘要：
设$μ$是某个可测空间$\{W=\{w\},{\mathcal{B}}(W)\}$上的高斯测度，$ν$是同一空间上关于$ν$绝对连续的测度.本文综述了在$W$空间上构造一个变换$T$使得$Tw=w+u(w)$的问题，其中$u$在Cameron-Martin空间中取值，并且在$T$下的$μ$的像是$μ$ .此外，我们要求存在的变换$T$属于某些特定的类。
英文摘要：
Let $μ$ be a Gaussian measure on some measurable space $\{W=\{w\},{\mathcal{B}}(W)\}$ and let $ν$ be a measure on the same space which is absolutely continuous with respect to $ν$. 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 $μ$ under $T$ is $μ$. In addition we ask for the existence of transformations $T$ belonging to some particular classes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
