Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-Ergodic Case

Abstract

We consider the parameter estimation problem for the non-ergodic fractional Ornstein- Uhlenbeck process defined as dXt = θXtdt + dBt, t≥ 0, with a parameter θ > 0, where B is a fractional Brownian motion of Hurst index H ∈ ( 1/2 , 1). We study the consistency and the asymptotic distributions of the least squares estimator ?? of θ based on the observation {Xs, s ∈ [0, t]} as t → ∞.