Statistical inference for Vasicek-type model driven by Hermite processes

Abstract
Let denote a Hermite process of order and self-similarity parameter . This process is -self-similar, has stationary increments and exhibits long-range dependence. When , it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as . In this paper, we deal with the following Vasicek-type model driven by : \[ X_0=0,\quad dX_t = a(b - X_t)dt +dZ_t^{q, H}, \qquad t \geq 0, \] where and are considered as unknown drift parameters. We provide estimators for and based on continuous-time observations. For all possible values of and , we prove strong consistency and we analyze the asymptotic fluctuations.
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