On drift parameter estimation for reflected fractional Ornstein-Uhlenbeck processes

摘要

We consider a reflected Ornstein-Uhlenbeck process X driven by a fractional Brownian motion with Hurst parameter H is an element of(0, 1/2) boolean OR (1/2, 1) . Our goal is to estimate an unknown drift parameter alpha is an element of(-infinity, infinity) on the basis of continuous observation of the state process. We establish Girsanov theorem for the process X, derive the standard maximum likelihood estimator of the drift parameter alpha, and prove its strong consistency and asymptotic normality. As an improved estimator, we obtain the explicit formulas for the sequential standard maximum likelihood estimator and its mean squared error by assuming the process is observed until a certain information reaches a specified precision level. The estimator is shown to be unbiased, uniformly normally distributed, and efficient in the mean square error sense.