Convergence in Dirichlet Law of Certain Stochastic Integrals

Abstract

Recently, Nicolas Bouleau has proposed an extension of the Donsker's invariance principle in the framework of Dirichlet forms. He proves that an erroneous random walk of i.i.d random variables converges in Dirichlet law toward the Ornstein-Uhlenbeck error structure on the Wiener space. The aim of this paper is to extend this result to some families of stochastic integrals.