%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=nn, 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 √nn(-θ) and √nn(-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.