Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media

Tomasz Srokowski

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 7, 1057-1066

Abstract: The Lévy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable diffusion coefficient, is solved in the diffusion limit. That solution resolves itself to the stretched Gaussian when the order parameter μ→2. The truncation of the Lévy flights, in the exponential and power-law form, is introduced and the corresponding random walk process is simulated by the Monte Carlo method. The stretched Gaussian tails are found in both cases. The time which is needed to reach the limiting distribution strongly depends on the jumping rate parameter. When the cutoff function falls slowly, the tail of the distribution appears to be algebraic.

Keywords: Diffusion; Fractional equation; Truncated Lévy flights (search for similar items in EconPapers)
Date: 2009
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:7:p:1057-1066

DOI: 10.1016/j.physa.2008.12.059

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