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arXiv · 1907.05631

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

Meryem Slaoui·Ciprian A. Tudor
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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) 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.

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Meryem Slaoui, Ciprian A. Tudor. 2019-07-12. Limit behavior of the Rosenblatt Ornstein-Uhlenbeck process with respect to the Hurst index. https://arxiv.org/abs/1907.05631

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