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

D. Feyel·A. S. Ustunel
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Abstract

Let $(W,H,μ)$ 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.

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D. Feyel, A. S. Ustunel. 2004-09-16. Some remarks about the positivity of random variables on a Gaussian probability space. https://arxiv.org/abs/math/0409268

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