分数布朗运动驱动的自排斥扩散的渐近行为与参数估计

Asymptotic Behavior and Estimation of Self-Repelling Diffusion Driven by Fractional Brownian Motion (fBm)

在本文中,我们研究了Hurst指数的分数布朗运动驱动的自排斥扩散随机微分方程解的长时间行为以及当ν=0时θ最小二乘估计θ^,并讨论了θ^相合性和θ^T-θ的渐进分布。

In this paper, we consider a self-repelling diffusion driven by a fractional Brownian motion with Hurst index , , we prove asymptotic behavior of the solution and the strong consistent of θ^ when ν=0, we also obtain the asymptotic distribution of θ^T-θ.