arXiv subjects
Publications and source records attributed to A. S. Üstünel.
The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of Paul Malliavin.
We define, in the frame of an abstract Wiener space, the notions of convexity and of concavity for the equivalence classes of random variables. As application we show that some important inequalities of the finite dimensional case have their natural counterparts in this setting.
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.