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June 2013 Drift parameter estimation for a reflected fractional Brownian motion based on its local time
Yaozhong Hu, Chihoon Lee
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J. Appl. Probab. 50(2): 592-597 (June 2013). DOI: 10.1239/jap/1371648963

Abstract

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.

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Yaozhong Hu. Chihoon Lee. "Drift parameter estimation for a reflected fractional Brownian motion based on its local time." J. Appl. Probab. 50 (2) 592 - 597, June 2013. https://doi.org/10.1239/jap/1371648963

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1301.60050
MathSciNet: MR3102502
Digital Object Identifier: 10.1239/jap/1371648963

Subjects:
Primary: 60G22
Secondary: 62M09, 90B18

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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