由α-稳定过程驱动的线性自排斥扩散过程的渐近行为和参数估计

Asymptotic Behavior and Parameter Estimation of the Linear Self-Repelling Diffusion Driven by α-Stable Motion

设为一维-稳定模型且。本文主要研究如下线性自排斥扩散的长时间行为和参数估计:,其中、是两个未知参数且。当且t趋于无穷大时,对任意,我们有和几乎处处成立,其中。在连续观测条件下,建立和的最小二乘估计讨论其相合性与渐近分布。

Let be an -stable motion of one-dimension with . In this paper, we consider large time behaviors and parameter estimation of the linear self-repelling diffusion of the forms where and are two unknown parameters. When and t tends to infinity, we show that the convergence and hold almost surely for all , where . The least squares estimates of and are established to discuss their coincidence and asymptotic distributions under continuous observation conditions.