Stochastic scalar conservation laws driven by rough paths
- Authors: Peter K. Friz, Benjamin Gess
- Preprint year: 2014
- First public date: 2014-03-26
- arXiv: 1403.6785
- Status: Published
- Publication type: Journal article
- Publication year: 2016
- Journal: Annales de l'Institut Henri Poincaré / C, 33 (2016) 4, pp. 933-963
- DOI: 10.1016/j.anihpc.2015.01.009
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.