Stochastic description of delayed systems

TL;DR

This paper develops analytical methods for stochastic birth-death processes with delays, including stochastic delays with arbitrary distributions, to understand how delay influences fluctuations and correlations in non-Markovian systems.

Contribution

It introduces new approaches for analyzing non-Markovian stochastic systems with both constant and stochastic delays, expanding beyond previous methods limited to simpler cases.

Findings

Delay affects fluctuations and correlations in stochastic systems

Analytical methods applicable to arbitrary delay distributions

Insights into non-Markovian stochastic dynamics

Abstract

We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with arbitrary probability distributions. The interplay between stochasticity and delay and, in particular, the effects of delay in the fluctuations and time correlations are discussed.