Journal of Applied Probability

Drift parameter estimation for a reflected fractional Brownian motion based on its local time

Yaozhong Hu and Chihoon Lee

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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.

Article information

J. Appl. Probab., Volume 50, Number 2 (2013), 592-597.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 62M09: Non-Markovian processes: estimation 90B18: Communication networks [See also 68M10, 94A05]

Parameter estimation fractional Brownian motion reflected process strong consistency queueing model asymptotic normality


Hu, Yaozhong; Lee, Chihoon. Drift parameter estimation for a reflected fractional Brownian motion based on its local time. J. Appl. Probab. 50 (2013), no. 2, 592--597. doi:10.1239/jap/1371648963.

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