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First Steps in Random WalksFrom Tools to Applications$
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J. Klafter and I. M. Sokolov

Print publication date: 2011

Print ISBN-13: 9780199234868

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199234868.001.0001

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Lévy flights

Lévy flights

(p.97) 7 Lévy flights
First Steps in Random Walks

J. Klafter

I.M. Sokolov

Oxford University Press

This chapter returns to simple random walks and considers the case when the mean squared displacement in one step diverges. In the case of step length distributions with power‐law tails the corresponding limiting densities converge to Levy distributions; this case is therefore deemed Levy flight. The chapter first considers the properties of Levy distributions and then discusses space‐fractional generalization of the diffusion equation for such random walks. We moreover shortly discuss the first passage properties of such processes and gives recipes for simulation of Levy random variables useful in applications.

Keywords:   Levy distributions, space‐fractional diffusion equation, leapover, simulation of Levy variables

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