Stochastic scalar conservation laws driven by rough paths
Analysis of PDEs
2014-03-27 v1 Probability
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
@article{arxiv.1403.6785,
title = {Stochastic scalar conservation laws driven by rough paths},
author = {Peter K. Friz and Benjamin Gess},
journal= {arXiv preprint arXiv:1403.6785},
year = {2014}
}
Comments
29 pages