Least Squares Estimation for α-Fractional Bridge with Discrete Observations. (23rd January 2014) - Shen, Guangjun; Yin, Xiuwei
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 → ∞ .