%A Khalifa ES-SEBAIY, Fares ALAZEMI, Mishari AL-FORAIH
%T LEAST SQUARES TYPE ESTIMATION FOR DISCRETELY OBSERVED NON-ERGODIC GAUSSIAN ORNSTEIN-UHLENBECK PROCESSES
%0 Journal Article
%D 2019
%J 数学物理学报(英文版)
%R 10.1007/s10473-019-0406-0
%P 989-1002
%V 39
%N 4
%U {http://121.43.60.238/sxwlxbB/CN/abstract/article_15927.shtml}
%8 2019-08-25
%X In this article, we consider the drift parameter estimation problem for the nonergodic Ornstein-Uhlenbeck process defined as dXt=θXtdt + dGt, t ≥ 0 with an unknown parameter θ > 0, where G is a Gaussian process. We assume that the process {Xt, t ≥ 0} is observed at discrete time instants t1=△n,…, tn=n△n, and we construct two least squares type estimators and for θ on the basis of the discrete observations {Xti, i=1,…, n} as n → ∞. Then, we provide sufficient conditions, based on properties of G, which ensure that and are strongly consistent and the sequences √n△n(-θ) and √n△n(-θ) are tight. Our approach offers an elementary proof of[11], which studied the case when G is a fractional Brownian motion with Hurst parameter H ∈ (1/2, 1). As such, our results extend the recent findings by[11] to the case of general Hurst parameter H ∈ (0, 1). We also apply our approach to study subfractional Ornstein-Uhlenbeck and bifractional Ornstein-Uhlenbeck processes.