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We discuss several properties of the generalized Hermite process, which is a non-Gaussian self-similar processes with self-similarity index belonging to the whole interval. We also define Wiener integral with respect to this process and as an application, we define and study its associated Ornstein–Uhlenbeck process.

Generalized Wiener–Hermite integrals and rough non-Gaussian Ornstein–Uhlenbeck process