On an extension of the Hilbertian central limit theorem to Dirichlet forms.

In a recent paper, Bouleau provides a new tool, based on the language of Dirichlet forms, to study the errors propagation and reinforce the historical approach of Gauss. As the classical central limit theorem is a theoric justification of the employment of normal laws in statistics, the aim of this article is to underline the importance of certain classes of error structures by asymptotic arguments. Thus, we extend the notions of independence and convergence in distribution for random variables in order to prove a refinement of the hilbertian central limit theorem that highlights the fundamental role of the error structures of the Ornstein-Ulhenbeck type.