Parrondo-like behavior in continuous-time random walks with memory

TL;DR

This paper demonstrates that combining two unbiased continuous-time random walks, one with memory, can produce a process with a drift, illustrating a Parrondo-like paradox in stochastic processes with memory.

Contribution

It introduces a novel continuous-time random walk model with memory that exhibits Parrondo-like behavior when combined with noise.

Findings

Combination of unbiased CTRWs with memory yields a process with drift.

The phenomenon is analogous to Parrondo's paradox.

Memory in CTRWs is crucial for the observed effect.

Abstract

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 Parrondo's paradox in game theory