Parrondo-Like Behavior in Continuous-Time Random Walks with Periodically Alternating Jumps

Abstract

As a natural generalization of the discrete-time random walk, the continuous-time random walk (CTRW) has been applied to stochastic models with random dynamics in various fields. In this paper, we show that the deterministic alternation of two unbiased CTRWs can lead to a phenomenon similar to the Parrondo paradox, in which the asymptotic mean drift of the combined CTRW becomes positive or negative depending on the parameter values. This extends the case in which the paradox occurs due to the random combination of two CTRWs with memory shown by Montero [Phys. Rev. E 84 (2011) 051139].