Multivariate Gaussian approximations on Markov chaoses

Simon Campese (1) , Ivan Nourdin (2) , Giovanni Peccati (2) , Guillaume Poly (3)

1 Università degli Studi di Roma Tor Vergata [Roma, Italia] = University of Rome Tor Vergata [Rome, Italy] = Université de Rome Tor Vergata [Rome, Italie]
2 FSTC - Faculté des Sciences, de la Technologie et de la Communication
3 IRMAR - Institut de Recherche Mathématique de Rennes

We prove a version of the multidimensional Fourth Moment Theorem for chaotic random vectors, in the general context of diffusion Markov generators. In addition to the usual componentwise convergence and unlike the infinite-dimensional Ornstein-Uhlenbeck generator case, another moment-type condition is required to imply joint convergence of of a given sequence of vectors.

Keywords: Markov Diffusion Generator; Fourth Moment Theorem; Multivariate Normal Approximations

Domains: Probability [math.PR]

Simon Campese, Ivan Nourdin, Giovanni Peccati, Guillaume Poly. Multivariate Gaussian approximations on Markov chaoses. 2015. ⟨hal-01219698⟩