First passage time moments of asymmetric Lévy flights

First passage time moments of asymmetric Lévy flights

We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage time probability density function for different values of the in...

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Veröffentlicht in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-07, Vol.53 (27), p.275002
Hauptverfasser: Padash, Amin, Chechkin, Aleksei V, Dybiec, Bartłomiej, Magdziarz, Marcin, Shokri, Babak, Metzler, Ralf
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first passage time moments
fractional diffusion equation
Lévy flight
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container_issue 27
container_start_page 275002
container_title Journal of physics. A, Mathematical and theoretical
container_volume 53
creator Padash, Amin
Chechkin, Aleksei V
Dybiec, Bartłomiej
Magdziarz, Marcin
Shokri, Babak
Metzler, Ralf
description We investigate the first-passage dynamics of symmetric and asymmetric Lévy flights in semi-infinite and bounded intervals. By solving the space-fractional diffusion equation, we analyse the fractional-order moments of the first-passage time probability density function for different values of the index of stability and the skewness parameter. A comparison with results using the Langevin approach to Lévy flights is presented. For the semi-infinite domain, in certain special cases analytic results are derived explicitly, and in bounded intervals a general analytical expression for the mean first-passage time of Lévy flights with arbitrary skewness is presented. These results are complemented with extensive numerical analyses.
doi_str_mv 10.1088/1751-8121/ab9030
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subjects first passage time moments
fractional diffusion equation
Lévy flight
title First passage time moments of asymmetric Lévy flights
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