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
摘要: 设Ma为一维a-稳定模型且1 < a < 2，本文考虑线性自吸引扩散，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。
Abstract: 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.
文章引用：陈香小, 陆允生, 闫理坦. 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[J]. 应用数学进展, 2021, 10(11): 3969-3982. https://doi.org/10.12677/AAM.2021.1011422

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