Let Z denote a Hermite process of order q≥1 and self-similarity
parameter H∈(21,1). This process is H-self-similar, has
stationary increments and exhibits long-range dependence. When q=1, it
corresponds to the fractional Brownian motion, whereas it is not Gaussian as
soon as q≥2. In this paper, we deal with a Vasicek-type model driven by
Z, of the form dXt=a(b−Xt)dt+dZt. Here, a>0 and b∈R are considered as unknown drift parameters. We provide estimators
for a and b based on continuous-time observations. For all possible values
of H and q, we prove strong consistency and we analyze the asymptotic
fluctuations.Comment: 19 pages, revised according to referee's repor