Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variables

in Progress in Probability (2016), 71

Fourth Moment Theorems for Markov diffusion generators

in Journal of Functional Analysis (2014), 266(4), 23412359

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion ... [more ▼]

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13] (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We are not only able to drastically simplify all of its previous proofs, but also to provide new settings of diffusive generators (Laguerre, Jacobi) where such a criterion holds. Convergence towards Gamma and Beta distributions under moment conditions is also discussed. [less ▲]

Absolute continuity and convergence of densities for random vectors on Wiener chaos

in Electronic Journal of Probability (2013), 18(22), 1--19

bsolute continuity of Markov chains ergodic measures by Dirichlet forms methods

E-print/Working paper (2012)