The Ornstein–Uhlenbeck process driven by the Hermite–Ornstein–Uhlenbeck process
Pub. online: 10 February 2026
Type: Research Article
Open Access
Open Access
Received
15 October 2025
15 October 2025
Revised
26 January 2026
26 January 2026
Accepted
26 January 2026
26 January 2026
Published
10 February 2026
10 February 2026
Abstract
In this paper, a non-Gaussian Ornstein–Uhlenbeck process driven by a Hermite–Ornstein–Uhlenbeck process is introduced, which belongs to the qth Wiener chaos. A systematic procedure to identify the drift parameter θ and the Hurst parameter H is given based on the study of the limit behavior of its quadratic variations. Estimators for these two parameters and their asymptotic properties are studied.
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