On the structure of Gaussian random variables
نویسنده
چکیده
We study when a given Gaussian random variable on a given probability space (Ω,F , P ) is equal almost surely to β1 where β is a Brownian motion defined on the same (or possibly extended) probability space. As a consequence of this result, we prove that the distribution of a random variable in a finite sum of Wiener chaoses (satisfying in addition a certain property) cannot be normal. This result also allows to understand better a characterization of the Gaussian variables obtained via Malliavin calculus. 2000 AMS Classification Numbers: 60G15, 60H05, 60H07.
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