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

Abstract

We study the convergence in distribution, as $H\to \frac{1}{2}$ and as $H\to 1$, of the integral ${\int }_{\mathbb{R}}f(u)d{Z}^H(u)$, where $Z^H$ is a Rosenblatt process with self-similarity index $H\in \left(\frac{1}{2},1\right)$ 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.

References in corpus (1)

• Central limit theorems for sequences of multiple stochastic integrals