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Large deviation principles for first-order scalar conservation laws with stochastic forcing / Jiang-lun, Wu

The Annals of Applied Probability, Volume: 30, Issue: 1, Pages: 324 - 367

Swansea University Author: Jiang-lun, Wu

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DOI (Published version): 10.1214/19-aap1503

Abstract

In this paper, we established the Freidlin-Wentzell type large deviation principles for first- order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order co...

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Published in: The Annals of Applied Probability
ISSN: 1050-5164 2168-8737
Published: Institute of Mathematical Statistics Institute of Mathematical Statistics 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa48584
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Abstract: In this paper, we established the Freidlin-Wentzell type large deviation principles for first- order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conser- vation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.
Keywords: large deviations; first-order conservation laws; weak convergence approach; kinetic solution.
Issue: 1
Start Page: 324
End Page: 367