Fractional diffusion equation for a power-law-truncated Lévy process

I.m Sokolov, A.v Chechkin and J Klafter

Physica A: Statistical Mechanics and its Applications, 2004, vol. 336, issue 3, 245-251

Abstract: Truncated Lévy flights are stochastic processes which display a crossover from a heavy-tailed Lévy behavior to a faster decaying probability distribution function (pdf). Putting less weight on long flights overcomes the divergence of the Lévy distribution second moment. We introduce a fractional generalization of the diffusion equation, whose solution defines a process in which a Lévy flight of exponent α is truncated by a power-law of exponent 5−α. 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.

Keywords: Truncated Lévy flights; Fractional kinetics; Distributed-order diffusion equation (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:336:y:2004:i:3:p:245-251

DOI: 10.1016/j.physa.2003.12.044

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