Parameter estimation based on discrete observations of fractional Ornstein–Uhlenbeck process of the second kind

Fractional Ornstein–Uhlenbeck process of the second kind (fOU2) is a solution of the Langevin equation (Formula presented.) with a Gaussian driving noise (Formula presented.), where (Formula presented.) and B is a fractional Brownian motion with Hurst parameter H∈(0,1). In this article we consider the case H>12, and by using the ergodicity of fOU2 process we construct consistent estimators for the drift parameter θ based on discrete observations in two possible cases:(i) the Hurst parameter H is known and (ii) the Hurst parameter H is unknown. Moreover, using Malliavin calculus techniques we prove central limit theorems for our estimators which are valid for the whole range H∈(12,1). © 2014, Springer Science+Business Media Dordrecht.