Fractional Diffusion Equation for a Power-Law-Truncated Levy Process
Condensed Matter
2009-11-10 v1
Abstract
Truncated Levy flights are stochastic processes which display a crossover from a heavy-tailed Levy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the Levy distribution second moment. We introduce a fractional generalization of the diffusion equation, whose solution defines a process in which a Levy flight of exponent alpha is truncated by a power-law of exponent 5 - alpha. A closed form for the characteristic function of the process is derived. The pdf of the displacement slowly converges to a Gaussian in its central part showing however a power law far tail. Possible applications are discussed.
Cite
@article{arxiv.cond-mat/0309464,
title = {Fractional Diffusion Equation for a Power-Law-Truncated Levy Process},
author = {I. M. Sokolov and A. V. Chechkin and J. Klafter},
journal= {arXiv preprint arXiv:cond-mat/0309464},
year = {2009}
}