https://doi.org/10.1140/epjb/e2017-80348-4
Regular Article
Continuous-time random walks with reset events*
Historical background and new perspectives
1 Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB), Martí i Franquès 1, 08028 Barcelona, Spain
2 Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Spain
3 Departamento de Matemáticas & Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Plaza Merced s/n, 37008 Salamanca, Spain
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Received: 15 June 2017
Received in final form: 4 July 2017
Published online: 25 September 2017
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.
Contribution to the Topical Issue “Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook”, edited by Ryszard Kutner and Jaume Masoliver.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2017
