期刊
JOURNAL OF APPLIED PROBABILITY
卷 41, 期 3, 页码 623-638出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1239/jap/1091543414
关键词
operator self-similar process; continuous-time random walk
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.
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