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