2014/03/26 by Friz, Peter K., Gess, Benjamin
#35L65 #35R60 #Analysis of PDEs (math.AP) #FOS: Mathematics #H6015 #Probability (math.PR)
paper · doi:10.48550/arxiv.1403.6785
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.