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2013-01-16

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/34148

Monotonic continuous-time random walks with drift and stochastic reset events

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http://dx.doi.org/10.1103/PhysRevE.87.012116

Abstract

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

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Processos estocàstics, Mètode de Montecarlo, Transformació de Laplace

Subject (English)

Stochastic processes, Monte Carlo method, Laplace transformation

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Articles publicats en revistes (Física de la Matèria Condensada)

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MONTERO TORRALBO, Miquel and VILLARROEL, Javier. Monotonic continuous-time random walks with drift and stochastic reset events. Physical Review E. 2013. Vol. 87, num. 012116-1-012116-14. ISSN 1539-3755. [consulted: 7 of August of 2026]. Available at: https://hdl.handle.net/2445/34148

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