Two properties of vectors of quadratic forms in Gaussian random variables

Vladimir I. Bogachev, Egor D. Kosov, Ivan Nourdin, Guillaume Poly

Published 2013-05-26Version 1

We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some interesting consequences. Our second result gives a characterization of limits in law for sequences of such vectors.