Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes

TL;DR

This paper introduces a perturbative field theory framework to analyze extreme events and survival probabilities in non-Markovian stochastic processes, accounting for interactions and correlated noise.

Contribution

It develops a systematic, diagrammatic approach using Doi-Peliti and Martin-Siggia-Rose formalisms to study non-Markovian processes, extending analysis beyond Markovian assumptions.

Findings

Applied to Brownian motion with self-correlated noise

Calculated survival probability distribution for non-Markovian processes

Provided a new perturbative method for extreme event analysis

Abstract

We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose formalism. This field theory treats interactions and the effect of external, possibly self-correlated noise in a perturbation about a Markovian process, thereby providing a systematic, diagrammatic approach to extreme events. We apply the formalism to Brownian Motion and calculate its survival probability distribution subject to self-correlated noise.