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

S. V. Buldyrev, S. Havlin, A. Ya Kazakov, M. G.E. Da Luz, E. P. Raposo, H. E. Stanley, G. M. Viswanathan

Research output: Contribution to journalArticlepeer-review

117 Scopus citations

Abstract

The problems of Levy flights and Levy walks on a finite interval with absorbing boundaries were discussed. The Fredholm integral equations and Laplace transform in the temporal domain were used for the solution of mean time of travel before absorption for discrete Levy flights and Levy walks. The fractional differential equations were shown to be good approximations for Levy flights with absorbing boundaries for α>2. It was also shown that these approximations break down in the vicinity of the boundaries when α=2.

Original languageEnglish
Article number041108
Pages (from-to)411081-4110811
Number of pages3699731
JournalPhysical Review E
Volume64
Issue number4 I
StatePublished - Oct 2001

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