Dotti, Sylvain; Vovelle, Julien Convergence of approximations to stochastic scalar conservation laws. (English) Zbl 1397.65016 Arch. Ration. Mech. Anal. 230, No. 2, 539-591 (2018). Summary: We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a stochastic scalar conservation law. The weak probabilistic convergence mode is convergence in law, the most natural in this context. We use also a kinetic formulation and martingale methods. Our result is applied to the convergence of the finite volume method in the companion paper of the authors [“Convergence of the finite volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation”, Preprint, arXiv:1611.00983]. Cited in 1 ReviewCited in 9 Documents MSC: 65C30 Numerical solutions to stochastic differential and integral equations 35R60 PDEs with randomness, stochastic partial differential equations 60G57 Random measures 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35L65 Hyperbolic conservation laws 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs PDFBibTeX XMLCite \textit{S. Dotti} and \textit{J. Vovelle}, Arch. Ration. Mech. Anal. 230, No. 2, 539--591 (2018; Zbl 1397.65016) Full Text: DOI arXiv HAL References: [1] Bauzet, C, Time-splitting approximation of the Cauchy problem for a stochastic conservation law, Math. Comput. 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