Survival probabilities in time-dependent random walks

TL;DR

This paper studies how periodic time-dependent changes in jumping probabilities affect the survival chances of biased random walkers near an absorbing boundary, revealing that increased oscillation amplitude reduces their lifetime.

Contribution

It provides a novel analysis of survival probabilities in time-dependent random walks with periodic transition probabilities, extending understanding of such stochastic processes.

Findings

Survival probability decreases with higher oscillation amplitude.

The typical lifetime of walkers shortens as oscillation amplitude increases.

Results are applicable to complex adaptive systems.

Abstract

We analyze the dynamics of random walks in which the jumping probabilities are periodic {\it time-dependent} functions. In particular, we determine the survival probability of biased walkers who are drifted towards an absorbing boundary. The typical life-time of the walkers is found to decrease with an increment of the oscillation amplitude of the jumping probabilities. We discuss the applicability of the results in the context of complex adaptive systems.