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Dong, Zhao; Wu, Jiang-Lun; Zhang, Rangrang; Zhang, Tusheng

Large deviation principles for first-order scalar conservation laws with stochastic forcing. (English) Zbl 1465.60025

Ann. Appl. Probab. 30, No. 1, 324-367 (2020).
Summary: 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.

Cited in 21 Documents

MSC:

60F10 Large deviations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)

Keywords:

large deviations; first-order conservation laws; weak convergence approach; kinetic solution
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Full Text: DOI arXiv Euclid

References:

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