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.

24 pages, 4 figures; added figures, comments and references

References in corpus (3)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Extremal statistics for stochastic resetting systems
• Path integral formulation of fractional Brownian motion for general Hurst exponent