Limit theorems for nonlinear functionals of Volterra processes via white noise analysis

I. Nourdin (1) , S. Darses , D. Nualart

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the classical convergence results of the 1980s due to Breuer, Dobrushin, Giraitis, Major, Surgailis and Taqqu, as well as the recent advances concerning the construction of a Levy area for fBm due to Coutin, Qian and Unterberger.

Domaines: Probabilités [math.PR]

I. Nourdin, S. Darses, D. Nualart. Limit theorems for nonlinear functionals of Volterra processes via white noise analysis. Bernoulli, 2010, 16 (4), pp.1262-1293. ⟨10.3150/10-BEJ258⟩. ⟨hal-00555392⟩