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

Part of: Stochastic processes Inference from stochastic processes Operations research and management science

Published online by Cambridge University Press:  30 January 2018

Yaozhong Hu  and
Chihoon Lee
Yaozhong Hu*
Affiliation:
University of Kansas
Chihoon Lee*
Affiliation:
Colorado State University
*
∗ Postal address: Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA. Email address: hu@math.ku.edu
∗∗ Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA. Email address: chihoon@stat.colostate.edu
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Abstract

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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.

Keywords

Parameter estimationfractional Brownian motionreflected processstrong consistencyqueueing modelasymptotic normality

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 62M09: Non-Markovian processes 90B18: Communication networks
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 592 - 597
Copyright
© Applied Probability Trust 

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