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

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.