HIGHLIGHTS
- What: Utilizing tools of Malliavin and stochastic calculus in Wiener space the authors show that this is a contraction in various settings where analogous questions for optimal maps are open. contraction properties of enable the authors to prove functional inequalities in Euclidean spaces which are either completely new or improve on current results. The authors show that optimal maps and causal optimal maps (which are related to maps) between Wiener measure and other target measures on Wiener space exhibit very different behaviors. The authors focus on several mechanisms which in principle could facilitate such contractions. In Sect . . .
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