Representation of random walk in fractal space-time

Ryutaro Kanno

Physica A: Statistical Mechanics and its Applications, 1998, vol. 248, issue 1, 165-175

Abstract: To analyze the anomalous diffusion on a fractal structure with fractal in the time axis, we propose a statistical representation given by a path integral method in arbitrary fractal space-time. Using the method, we can understand easily several properties of the non-Gaussian-type behavior, and a differential equation for the path integral is derived. Finally, to check the validity of this theory, analytical results in this paper are applied to the random walk on the two-dimensional Sierpinski carpet, which agree precisely with numerical results by Monte Carlo simulations in the paper of Fujiwara and Yonezawa [Phys. Rev. E 51 (1995) 2277].

Keywords: Non-Gaussian process; Anomalous diffusion; Path integral; Fractal nature; Hausdorff length (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:248:y:1998:i:1:p:165-175

DOI: 10.1016/S0378-4371(97)00422-6

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