Continuous-time random walks with reset events: Historical background and new perspectives

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 res...

Full description

Saved in:
Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2017-09, Vol.90 (9)
Main Authors: Montero, Miquel, Maso-Puigdellosas, Axel, Villarroel, Javier
Format: Article
Language:English
Subjects:
Stochastic processes
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e01-04-4