On drift parameter estimation for reflected fractional Ornstein–Uhlenbeck processes. Issue 5 (3rd July 2016)

• Record Type: Journal Article
• Authors: Lee, Chihoon; Song, Jian
• Is Part Of: Stochastics. Volume 88:Issue 5(2016)
• Page Start: 751
• Page End: 778
• Publication Date: 2016-07-03
• Subjects: Reflected fractional Ornstein–Uhlenbeck processes -- fractional Brownian motion -- fractional calculus -- parameter estimation -- maximum likelihood estimator -- sequential maximum likelihood estimator; Primary: 60G22 -- Secondary: 60H30 -- 62M09 -- 90B22; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2016.1143472
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : We consider a reflected Ornstein–Uhlenbeck process X driven by a fractional Brownian motion with Hurst parameter . Our goal is to estimate an unknown drift parameter 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, 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.