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arXiv · 1507.05518

On stochastic conservation laws and Malliavin calculus

Kenneth Hvistendahl Karlsen·Erlend Briseid Storrøsten
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Abstract

For stochastic conservation laws driven by a semilinear noise term, we propose a generalization of the Kru\v{z}kov entropy condition by allowing the Kru\v{z}kov constants to be Malliavin differentiable random variables. Existence and uniqueness results are provided. Our approach sheds some new light on the stochastic entropy conditions put forth by Feng and Nualart [J. Funct. Anal., 2008] and Bauzet, Vallet, and Wittbold [J. Hyperbolic Differ. Equ., 2012].

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Kenneth Hvistendahl Karlsen, Erlend Briseid Storrøsten. 2015-07-20. On stochastic conservation laws and Malliavin calculus. https://arxiv.org/abs/1507.05518

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