Asymptotic behaviour on the linear self-interacting diffusion driven by α-stable motion
Asymptotic behaviour on the linear self-interacting diffusion driven by α-stable motion
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DOI：
10.1080/17442508.2020.1869239
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Xichao Sun;Litan Yan
中科院分区：
文献类型：
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作者：
Xichao Sun;Litan Yan
作为一种尝试，我们考虑由α-稳定运动驱动的线性自相互作用扩散，它是方程的解，并且是()上的α-稳定运动。这个过程类似于自吸引扩散(见Durrett-Rogers，Prob.理论相关领域92(1992)，337-349，和克兰斯顿-勒简，数学。安。303(1995)，87-93)。本文的主要目的是证明与解过程有关的一些极限定理。当我们证明它在分布上收敛到α稳定的随机变量时，当t趋于无穷大时，其中FOR和FOR。当我们证明，AS收敛于和A.S.时。对于所有人来说，在哪里和在哪里。
In this paper, as an attempt we consider the linear self-interacting diffusion driven by an α-stable motion, which is the solution to the equation where , and is an α-stable motion on ( ). The process is an analogue of the self-attracting diffusion (see Durrett-Rogers, Prob. Theory Related Fields 92 (1992), 337–349, and Cranston-Le Jan, Math. Ann. 303 (1995), 87–93.). The main object of this paper is to prove some limit theorems associated with the solution process for . When we show that converges to an α-stable random variable in distribution, as t tends to infinity, where for and for . When , for all we show that, as , converges to and a.s. for all , where and .