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Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes
- Source :
- Phys. Rev. Res. 4 (2022) 043197
- Publication Year :
- 2021
-
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.<br />Comment: 24 pages, 4 figures; added figures, comments and references
- Subjects :
- Condensed Matter - Statistical Mechanics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. Res. 4 (2022) 043197
- Publication Type :
- Report
- Accession number :
- edsarx.2109.03649
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevResearch.4.043197