考虑由Rosenblatt过程驱动的Omstein-Uhlenbeck过程X1=X0-θ∫0^tXsds+σZt^H的最小二乘估计。其中Zi^H是一个指数为H∈(1/2,1)的标准Rosenblatt过程,参数θ,σ〉0。在σ已知并且过程可以被连续观测的情况下,研究未知参数θ的最小二乘估计。
In this paper,we investigated the least squares estimation of the Ornstein-Uhlenbeck process X1=X0-θ∫0^tXsds+σZt^H, driven by Rosenblatt process,where Zi^H was a Rosenblatt process with Hurst index H ∈ (1/2,1) 0 and θ,σ〉0 were two parameters. When σ was known,we studied the least square estimator of the parameter θ under the continuous observation.