Limit behavior of the Rosenblatt Ornstein-Uhlenbeck process with respect to the Hurst index

Meryem Slaoui (1) , Ciprian A. Tudor (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

We study the convergence in distribution, as H → 1 2 and as H → 1, of the integral R f (u)dZ H (u), where Z H is a Rosenblatt process with self-similarity index H ∈ 1 2 , 1 and f is a suitable deterministic function. We focus our analysis on the case of the Rosenblatt Ornstein-Uhlenbeck process, which is the solution of the Langevin equation driven by the Rosenblatt process.

Mots clés: Wiener chaos; Rosenblatt process; cumulants; Hurst parameter

Domaines: Probabilités [math.PR]

Meryem Slaoui, Ciprian A. Tudor. Limit behavior of the Rosenblatt Ornstein-Uhlenbeck process with respect to the Hurst index. Theory of Probability and Mathematical Statistics, 2018. ⟨hal-02181050⟩