We consider the least square estimator for the parameters of Ornstein-Uhlenbeck processes

driven by the Hermite process Z ^q,H_s with order q ≥ 1 and a Hurst index H ∈ (½, 1), where the periodic functions φ_j(s),j = 1,⌦, k are bounded, and the real numbers μ_j, j = 1, …, k together with β > 0 are unknown parameters. We establish the consistency of a least squares estimation and obtain the asymptotic behavior for the estimator. We also introduce alternative estimators, which can be looked upon as an application of the least squares estimator. In terms of the fractional Ornstein-Uhlenbeck processes with periodic mean, our work can be regarded as its non-Gaussian extension.

我们考虑Ornstein-Uhlenbeck过程参数的最小二乘估计

由埃尔米特过程从动Ž ^Q，H_小号与顺序q ≥1和Hurst指数ħ其中周期函数φ∈（1/2，1），_Ĵ（小号），Ĵ = 1，⌦，ķ是有界的，和实际数μ _Ĵ，Ĵ = 1，...，ķ连同β > 0是未知参数。我们建立最小二乘估计的一致性，并获得估计的渐近行为。我们还介绍了替代估计量，可以将其视为最小二乘估计量的应用。就具有周期均值的分数阶Ornstein-Uhlenbeck过程而言，我们的工作可以视为其非高斯扩展。