Absolute continuity and convergence of densities for random vectors on Wiener chaos - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Probability Année : 2013

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

Résumé

The aim of this paper is to establish some new results on the absolute continuity and the convergence in total variation for a sequence of d-dimensional vectors whose components belong to a finite sum of Wiener chaoses. First we show that the probability that the determinant of the Malliavin matrix of such vectors vanishes is zero or one, and this probability equals to one is equivalent to say that the vector takes values in the set of zeros of a polynomial. We provide a bound for the degree of this annihilating polynomial improving a result by Kusuoka. On the other hand, we show that the convergence in law implies the convergence in total variation, extending to the multivariate case a recent result by Nourdin and Poly. This follows from an inequality relating the total variation distance with the Fortet-Mourier distance. Finally, applications to some particular cases are discussed.
Fichier principal
Vignette du fichier
tv-multidim.pdf (251.06 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00719845 , version 1 (21-07-2012)
hal-00719845 , version 2 (30-01-2013)

Identifiants

Citer

Ivan Nourdin, David Nualart, Guillaume Poly. Absolute continuity and convergence of densities for random vectors on Wiener chaos. Electronic Journal of Probability, 2013, 18 (22), 19 p. ⟨10.1214/EJP.v18-2181⟩. ⟨hal-00719845v2⟩
119 Consultations
161 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More