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Register a new userParrondo-like behavior in continuous-time random walks with memory
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Authors
Miquel Montero
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The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same of the Parrondos paradox in game theory
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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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In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous 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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