Least Squares Estimation for α-Fractional Bridge with Discrete Observations. (23rd January 2014)

• Record Type: Journal Article
• Authors: Shen, Guangjun; Yin, Xiuwei
• Other Names: Yan Litan Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-01-23
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/748376
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We consider a fractional bridge defined as d X t = - α (X t / ( T - t )) d t + d B t H, 0 ≤ t < T, where B H is a fractional Brownian motion of Hurst parameter H > 1 / 2 and parameter α > 0 is unknown. We are interested in the problem of estimating the unknown parameter α > 0 . Assume that the process is observed at discrete time t i = i Δ n, i = 0, …, n, and T n = n Δ n denotes the length of the "observation window." We construct a least squares estimator α ^ n of α which is consistent; namely, α ^ n converges to α in probability as n → ∞ .