Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.043197 |
| _version_ | 1797210582949036032 |
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| author | Benjamin Walter Gunnar Pruessner Guillaume Salbreux |
| author_facet | Benjamin Walter Gunnar Pruessner Guillaume Salbreux |
| author_sort | Benjamin Walter |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T10:12:54Z |
| format | Article |
| id | doaj.art-6cb1fc2152d44f5b97d9048bc9707a6b |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:12:54Z |
| publishDate | 2022-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-6cb1fc2152d44f5b97d9048bc9707a6b2024-04-12T17:27:08ZengAmerican Physical SocietyPhysical Review Research2643-15642022-12-014404319710.1103/PhysRevResearch.4.043197Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processesBenjamin WalterGunnar PruessnerGuillaume SalbreuxWe 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.http://doi.org/10.1103/PhysRevResearch.4.043197 |
| spellingShingle | Benjamin Walter Gunnar Pruessner Guillaume Salbreux Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes Physical Review Research |
| title | Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes |
| title_full | Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes |
| title_fullStr | Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes |
| title_full_unstemmed | Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes |
| title_short | Field theory of survival probabilities, extreme values, first-passage times, and mean span of non-Markovian stochastic processes |
| title_sort | field theory of survival probabilities extreme values first passage times and mean span of non markovian stochastic processes |
| url | http://doi.org/10.1103/PhysRevResearch.4.043197 |
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