Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes - Walter,B; Pruessner,G; Salbreux,G (Physical Review Research, 2022)
We provide a perturbative framework to calculate extreme events ofnon-Markovian processes, by mapping the stochastic process to a two-speciesreaction diffusion process in a Doi-Peliti field theory combined with theMartin-Siggia-Rose formalism. This field theory treats interactions and theeffect of external, possibly self-correlated noise in a perturbation about aMarkovian process, thereby providing a systematic, diagrammatic approach toextreme events. We apply the formalism to Brownian Motion and calculate itssurvival probability distribution subject to self-correlated noise.