Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes
File(s)
Published version
Author(s)
Walter, Benjamin
Pruessner, Gunnar
Salbreux, Guillaume
Type
Journal Article
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.
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.
Date Issued
2022-12-19
Date Acceptance
2022-10-31
Citation
Physical Review Research, 2022, 4, pp.1-21
ISSN
2643-1564
Publisher
American Physical Society
Start Page
1
End Page
21
Journal / Book Title
Physical Review Research
Volume
4
Copyright Statement
© 2022 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
License URL
Identifier
http://arxiv.org/abs/2109.03649v1
Subjects
cond-mat.stat-mech
cond-mat.stat-mech
Notes
21 pages, 2 figures
Publication Status
Published
Date Publish Online
2022-12-19