JournalsaihpcVol. 33, No. 4pp. 933–963

Stochastic scalar conservation laws driven by rough paths

  • Peter K. Friz

    Institut für Mathematik, Technische Universität Berlin & Weierstraß–Institut für Angewandte Analysis und Stochastik, Berlin, Germany

  • Benjamin Gess

    Department of Mathematics, University of Chicago, USA
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Abstract

We prove the existence and uniqueness of solutions to a class of stochastic scalar conservation laws with joint space–time transport noise and affine-linear noise driven by a geometric p-rough path. In particular, stability of the solutions with respect to the driving rough path is obtained, leading to a robust approach to stochastic scalar conservation laws. As immediate corollaries we obtain support theorems, large deviation results and the generation of a random dynamical system.

Cite this article

Peter K. Friz, Benjamin Gess, Stochastic scalar conservation laws driven by rough paths. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 4, pp. 933–963

DOI 10.1016/J.ANIHPC.2015.01.009