Some remarks about the positivity of random variables on a Gaussian probability space

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72488Let $(W,H,μ)$ be an abstract Wiener space and $L$ be a probability density of class LlogL. Using the measure transportation of Monge-Kantorovitch, we prove that the kernel of the projection of L on the second Wiener chaos defines an (Hilbert-Schmidt) operator which is lower bounded by another Hilbert-Schmidt operator.6 pagesProbability60H07, 60H05, 60H25, 46G12, 47H05Some remarks about the positivity of random variables on a Gaussian probability spacetext