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

Abstract

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.