Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time

We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long range dependent and self similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.