|Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes with Discrete Observations
Yaozhong Hu, University of Kansas, Department of Mathematics
Monday,November 7, 2011
4:00 p.m., room 223, Weber Bldg
Consider an Ornstein-Uhlenbeck process, $dX_t=-\theta X_t dt+\sigma dB^H_t$, driven by fractional Brownian motion $B^H$ with known Hurst parameter $H\ge \frac12$ and known variance $\si$. But the parameter $\th>0$ is unknown. Assume that the process $X_t$ is observed at discrete time instants $t=h, 2h, \cdots, nh$. We construct an estimator $\theta_n$ of $\theta$. We prove the almost sure convergence of $\theta_n$ of $\theta$. We also prove the central limit type theorem and the Berry-Esseen type theorems for this estimator. Our tool is to use recent results on Malliavin calculus. This is a joint work with Jian Song.