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

Details Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case

2011-02-27

arxiv.org/abs/1102.5491v1

Mathematics

Probability

13 pages

Scientific paper

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, 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 $t\rightarrow\infty$.

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