32 citations · 200 across the 40 of their papers we have counts for
5 papers · 1 filter
An invariance principle under the total variation distance
Ivan Nourdin, Guillaume Poly
Let be a sequence of i.i.d. random variables, with mean zero and variance one. Let . An old and celebrated result of Prohorov assert…
Two properties of vectors of quadratic forms in Gaussian random variables
Vladimir I. Bogachev, Egor D. Kosov, Ivan Nourdin +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 contin…
Fourth Moment Theorems for Markov Diffusion Generators
Ehsan Azmoodeh, Simon Campese, Guillaume Poly
Inspired by the insightful article arXiv:1210.7587, we revisit the Nualart-Peccati-criterion arXiv:math/0503598 (now known as the Fourth Moment Theorem) from the point of view of s…
Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variables
Ivan Nourdin, Guillaume Poly
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a noncons…
Generalization of the Nualart-Peccati criterion
Ehsan Azmoodeh, Dominique Malicet, Guillaume Mijoule +1
The celebrated Nualart-Peccati criterion [Ann. Probab. 33 (2005) 177-193] ensures the convergence in distribution toward a standard Gaussian random variable of a given sequence…