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Average time spent by Lévy flights and walks on an interval with absorbing boundaries

2001
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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Levy flights and Levy walks, respectively. Using fractional differential equations with a Riesz kernel, we find exact analytical expressions for both

doi:10.1103/physreve.64.041108
pmid:11690011
fatcat:v4rxilxeuzghxjynml5ac7a7fy