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February 2020 Large deviation principles for first-order scalar conservation laws with stochastic forcing
Zhao Dong, Jiang-Lun Wu, Rangrang Zhang, Tusheng Zhang
Ann. Appl. Probab. 30(1): 324-367 (February 2020). DOI: 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 conservation 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.

Citation

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Zhao Dong. Jiang-Lun Wu. Rangrang Zhang. Tusheng Zhang. "Large deviation principles for first-order scalar conservation laws with stochastic forcing." Ann. Appl. Probab. 30 (1) 324 - 367, February 2020. https://doi.org/10.1214/19-AAP1503

Information

Received: 1 July 2018; Revised: 1 February 2019; Published: February 2020
First available in Project Euclid: 25 February 2020

zbMATH: 07200530
MathSciNet: MR4068313
Digital Object Identifier: 10.1214/19-AAP1503

Subjects:
Primary: 60F10
Secondary: 60H15

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 1 • February 2020
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