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Continuous-time random walks with reset events

Historical background and new perspectives
  • Miquel MonteroEmail author
  • Axel Masó-Puigdellosas
  • Javier Villarroel
Regular Article
First Online:
Part of the following topical collections:
  1. Topical issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook

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.

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB)BarcelonaSpain
  2. 2.Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de BarcelonaBarcelonaSpain
  3. 3.Departamento de Matemáticas & Instituto Universitario de Física Fundamental y Matemáticas, Universidad de SalamancaSalamancaSpain

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