Continuous-time random walks with reset events

Miquel Montero (), Axel Masó-Puigdellosas and Javier Villarroel
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Axel Masó-Puigdellosas: Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB)
Javier Villarroel: Departamento de Matemáticas & Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 9, 1-10

Abstract: Abstract In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.

Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1140/epjb/e2017-80348-4

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