|Université Paris 6|
Pierre et Marie Curie
|Université Paris 7|
|CNRS U.M.R. 7599|
|``Probabilités et Modèles Aléatoires''|
Code(s) de Classification MSC:
Résumé: We generalize and give new proofs of four limit theorems for quadratic functionals of Brownian motion and Brownian bridge, recently obtained by Deheuvels and Martynov () by means of Karhunen-Loeve expansions. Our techniques involve basic tools of stochastic calculus, as well as classic theorems about weak convergence of Brownian functionals. We establish explicit connections with occupation times of Bessel processes, Poincaré's Lemma and the class of quadratic functionals of Brownian local times studied in .
Mots Clés: Brownian motion ; Brownian bridge ; Quadratic functionals ; Weak convergence ; Bessel processes ; Brownian local times.
Prépublication numéro: PMA-773