由Lévy过程驱动的加权自排斥扩散的长时间行为和统计推断  

Long Time Behavior and Statistical Inference of the Weighted Self-Repelling Diffusion Driven by Lévy Process

作　　者：鲁蕴涵 闫理坦[1] 

机构地区：[1]东华大学理学院,上海

出　　处：《应用数学进展》2024年第3期991-1001,共11页Advances in Applied Mathematics

摘　　要：假设是一个跳有界且界限为1的Lévy过程,生成三元组为。在本文中,我们考虑了由Lévy过程驱动的线性自排斥扩散方程,其中,和。这类过程是一类自交互扩散过程。我们研究了当t趋于无穷时解的长时间行为,发现它具有一种循环收敛性,这在此前的研究中尚未有类似的结论。进一步的,当w=0时在连续观测情况下,通过最小二乘法给出了方程参数的估计。我们证明了的估计量具有强相合性,并讨论了它的渐近分布。Let  be a Lévy process with jumps bounded by 1 and generating triplet . In this paper, as an attempt we consider the linear self-repelling diffusion driven by a Lévy process, , where  and the parameter . This process is similar to a type of self-interacting diffusion process. This paper studies the long time behaviour of the solution as t tends to infinity, and we find that it exhibits a cyclic convergence property, for which similar conclusions have not appeared in previous studies. In addition, when w=0, by using least squares method, we establish the strong consistency of the estimate  and discuss its asymptotic distribution under the consecutive observation.

关 键 词：LÉVY过程 自排斥扩散 长时间行为 参数估计 渐近分布 

分 类 号：O17[理学—数学]