Limit theorems for continuous-time random walks with infinite mean waiting times
Limit theorems for continuous-time random walks with infinite mean waiting times
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DOI：
10.1239/jap/1091543414
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发表时间：
2004-09-01
影响因子：
1
通讯作者：
Scheffler, HP
中科院分区：
文献类型：
--
作者：
Meerschaert, MM;Scheffler, HP
连续时间随机游走是一种简单的随机游走，服从于物理学中用于模拟异常扩散的更新过程。在本文中，我们表明，当更新之间的时间有无限的平均，标度极限是一个操作Levy运动从属于一个经典的稳定从属打击时间过程。极限过程的密度函数解决了一个分数柯西问题，一个分数偏微分方程的哈密尔顿混沌的推广。我们还建立了一个泛函极限定理的严格广义吸引域的满算子稳定的法律，这是一些独立的兴趣。
A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Levy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.