带有指数型扩散项Ornstein-Uhlenback过程的参数估计

Parameter Estimation for Fractional Ornstein-Uhlenbeck with Exponential Diffusion Term

在本文中,我们研究带有指数型扩散项分数布朗运动驱动的Ornstein-Uhlenbeck过程的最小二乘估计,其中Hurst指数H≥1/2 。dXt=-θXtdt+σectdBtH,我们讨论满足相合性以及当1/2≤H≤5/8时应用多重维纳积分的中心极限定理得到-θ的渐进分布。这个最小二乘估计同时可以推导出其它类型的估计量,例如可由函数∫0TXt2dt进行表示。

In this paper, we consider a least square estimator for the Ornstein-Uhlenbeck processes driven by fractional Brownian motion (fBm) with Hurst index H≥1/2 and exponential diffusion term. dXt=-θXtdt+σectdBtH, we prove the strong consistent of , and also obtain the asymptotic distribution of -θ, when 1/2≤H≤5/8, applying a central limit theorem for multiple Wiener integrals. This least square estimator can be used to study other estimators such as obtained by a function of ∫0TXt2dt .