| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: We establish necessary and sufficient conditions for a sequence of $d$% -dimensional vectors of multiple stochastic integrals $\mathbf{F}% _{d}^{k}=\left( F_{1}^{k},...,F_{d}^{k}\right) $, $k\geq 1$, to converge in distribution to a $d$-dimensional Gaussian vector $\mathbf{N}_{d}=\left( N_{1},...,N_{d}\right) $. In particular, we show that if the covariance structure of $\mathbf{F}_{d}^{k}$ converges to that of $\mathbf{N}_{d}$, then componentwise convergence implies joint convergence. These results extend to the multidimensional case the main theorem of Nualart and Peccati (2003).
Mots Clés: Multiple stochastic integrals ; Limit theorems ; Weak convergence ; Brownian motion.
Date: 2003-11-04
Prépublication numéro: PMA-861