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 $d{X}_t=\theta X_{t}dt+d{B}_t,t\ge 0$, with a parameter $\theta >0$, where $B$ is a fractional Brownian motion of Hurst index $H\in (1/2,1)$. We study the consistency and the asymptotic distributions of the least squares estimator ${\hat{\theta }}_t$ of $\theta$ based on the observation $\{X_s,s\in [0,t]\}$ as $t\to \infty$.

13 pages

References in corpus (1)

• Central limit theorems for sequences of multiple stochastic integrals