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arXiv · 1102.0444

Fractal Dimensions for Continuous Time Random Walk Limits

Mark M. Meerschaert·Erkan Nane·Yimin Xiao
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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.

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Mark M. Meerschaert, Erkan Nane, Yimin Xiao. 2011-02-03. Fractal Dimensions for Continuous Time Random Walk Limits. https://arxiv.org/abs/1102.0444

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