Fractal Dimensions for Continuous Time Random Walk Limits

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.

22 pages, 1 figure, submitted for publication, a minor correction in section 3.2

References in corpus (5)

• Coupled continuous time random walks in finance
• Anomalous diffusion in correlated continuous time random walks
• Brownian subordinators and fractional Cauchy problems
• Correlated continuous time random walks
• Continuous time random walk with correlated waiting times

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