α-稳定模型驱动的线性自吸引扩散过程中参数的最小二乘估计

Least Squares Estimation for the Linear Self-Attracting Diffusion Driven by α-Stable Motions

设Ma为一维a-稳定模型且1 ,其中θ、v是两个实参数且θ】0。本文的主要目的是在离散观测下,建立θ和v的最小二乘估计并讨论其相合性与渐近分布。

Let Ma be an α-stable motion of dimension one with . In this paper, we consider the self-attracting diffusion of the forms where θ>0 and v∈R are two unknown parameters. The main object of this paper is to study the least squares estimation of θ and ν under the discrete observation and discuss the consistency and asymptotic distributions of the two estimators.