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

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

2004-09-16

arxiv.org/abs/math/0409268v1

Mathematics

Probability

6 pages

Scientific paper

Let $(W,H,\mu)$ 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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