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arXiv · 2109.03649

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

Benjamin Walter·Gunnar Pruessner·Guillaume Salbreux
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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.

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Benjamin Walter, Gunnar Pruessner, Guillaume Salbreux. 2021-09-08. Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes. https://doi.org/10.1103/physrevresearch.4.043197

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