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

I. M. Sokolov, A. V. Chechkin, J. Klafter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)245-251
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume336
Issue number3-4
DOIs
StatePublished - 15 May 2004

Funding

FundersFunder number
Fonds der Chemichen Industrie

    Keywords

    • Distributed-order diffusion equation
    • Fractional kinetics
    • Truncated Lévy flights

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