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math.PR2004
Some remarks about the positivity of random variables on a Gaussian probability space
D. Feyel, A. S. Ustunel
Let be an abstract Wiener space and be a probability density of class LlogL. Using the measure transportation of Monge-Kantorovitch, we prove that the kernel of the p…
math.PR2004★ 1 cited
Solution of the Monge-Ampere Equation on Wiener Space for log-concave measures
D. Feyel, A. S. Ustunel
In this work we prove that the unique 1-convex solution of the Monge problem contructed from the solution of the Monge-Kantorovitch problem between the Wiener measure and a target…
math.PR2003★ 9 cited
The Monge-Kantorovitch Problem and Monge-Ampere Equation on Wiener Space
D. Feyel, A. S. Ustunel
We give the solution of the Monge-Kantorovitch problem on the Wiener space for the singular Wasserstein metric which is defined with respect to the distance of the underlying Camer…