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) dZ^{ 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.
Categories: math.PR