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Gel’fand-Yaglom type equations for calculating fluctuations around instantons in stochastic systems
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Schorlepp, Timo, Grafke, Tobias and Grauer, Rainer (2021) Gel’fand-Yaglom type equations for calculating fluctuations around instantons in stochastic systems. Journal of Physics A: Mathematical and Theoretical, 54 (23). 235003. doi:10.1088/1751-8121/abfb26 ISSN 1751-8113.
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Official URL: http://dx.doi.org/10.1088/1751-8121/abfb26
Abstract
In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential scaling. In this paper, we derive a general, closed form expression for the leading prefactor contribution of the fluctuations around the instanton trajectory for the computation of probability density functions of general observables. The key technique is applying the Gel'fand-Yaglom recursive evaluation method to the suitably discretized Gaussian path integral of the fluctuations, in order to obtain matrix evolution equations that yield the fluctuation determinant. We demonstrate agreement between these predictions and direct sampling for examples motivated from turbulence theory.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Instantons , Large deviations, Stochastic systems | |||||||||
| Journal or Publication Title: | Journal of Physics A: Mathematical and Theoretical | |||||||||
| Publisher: | IOP Publishing Ltd | |||||||||
| ISSN: | 1751-8113 | |||||||||
| Official Date: | 14 May 2021 | |||||||||
| Dates: |
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| Volume: | 54 | |||||||||
| Number: | 23 | |||||||||
| Article Number: | 235003 | |||||||||
| DOI: | 10.1088/1751-8121/abfb26 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 27 April 2021 | |||||||||
| Date of first compliant Open Access: | 27 April 2021 | |||||||||
| RIOXX Funder/Project Grant: |
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