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Continuous-time random walks with reset events

Author

Listed:
  • Miquel Montero

    (Departament de Física de la Matèria Condensada, Universitat de Barcelona (UB)
    Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona)

  • 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)

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.

Suggested Citation

  • Miquel Montero & Axel Masó-Puigdellosas & Javier Villarroel, 2017. "Continuous-time random walks with reset events," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(9), pages 1-10, September.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:9:d:10.1140_epjb_e2017-80348-4
    DOI: 10.1140/epjb/e2017-80348-4
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    Cited by:

    1. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    2. Konstantin Avrachenkov & Alexey Piunovskiy & Yi Zhang, 2018. "Hitting Times in Markov Chains with Restart and their Application to Network Centrality," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1173-1188, December.

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