On drift parameter estimation for reflected fractional Ornstein–Uhlenbeck processes

Chihoon Lee, Jian Song

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We consider a reflected Ornstein–Uhlenbeck process X driven by a fractional Brownian motion with Hurst parameter (Formula presented.). Our goal is to estimate an unknown drift parameter (Formula presented.) on the basis of continuous observation of the state process. We establish Girsanov theorem for the process X, derive the standard maximum likelihood estimator of the drift parameter (Formula presented.) , and prove its strong consistency and asymptotic normality. As an improved estimator, we obtain the explicit formulas for the sequential standard maximum likelihood estimator and its mean squared error by assuming the process is observed until a certain information reaches a specified precision level. The estimator is shown to be unbiased, uniformly normally distributed, and efficient in the mean square error sense.

Original languageEnglish
Pages (from-to)751-778
Number of pages28
JournalStochastics
Volume88
Issue number5
DOIs
StatePublished - 3 Jul 2016

Keywords

  • Reflected fractional Ornstein–Uhlenbeck processes
  • fractional Brownian motion
  • fractional calculus
  • maximum likelihood estimator
  • parameter estimation
  • sequential maximum likelihood estimator

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