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# Theory of Probability and Mathematical Statistics (Teoriya Imovirnostei ta Matematychna Statystyka)

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

### M. Slaoui, C. A. Tudor

Abstract: We study the convergence in distribution, as H→1/2 and as H→1, of the integral $\int_{\mathbb{R}} f(u) dZ^{H}(u)$, 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.

Keywords: Wiener chaos, Rosenblatt process, cumulants, Hurst parameter.

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