Fractal Dimensions for Continuous Time Random Walk Limits
Probability
2016-11-29 v2 Mathematical Physics
math.MP
Abstract
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner process (or time change) accounts for waiting times between jumps. This paper studies fractal properties of the sample functions of a time-changed process, and establishes some general results on the Hausdorff and packing dimensions of its range and graph. Then those results are applied to CTRW scaling limits.
Cite
@article{arxiv.1102.0444,
title = {Fractal Dimensions for Continuous Time Random Walk Limits},
author = {Mark M. Meerschaert and Erkan Nane and Yimin Xiao},
journal= {arXiv preprint arXiv:1102.0444},
year = {2016}
}
Comments
22 pages, 1 figure, submitted for publication, a minor correction in section 3.2