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

Yaozhong Hu, Chihoon Lee

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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.

Original languageEnglish
Pages (from-to)592-597
Number of pages6
JournalJournal of Applied Probability
Volume50
Issue number2
DOIs
StatePublished - Jun 2013

Keywords

  • Asymptotic normality
  • Fractional Brownian motion
  • Parameter estimation
  • Queueing model
  • Reflected process
  • Strong consistency

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