Multilevel Monte-Carlo for measure valued solutions

We propose a Multilevel Monte-Carlo (MLMC) method for computing entropy measure valued solutions of hyperbolic conservation laws. Sharp bounds for the narrow convergence of MLMC for the entropy measure valued solutions are proposed. An optimal work-vs-error bound for the MLMC method is derived assuming only an abstract decay criterion on the variance. Finally, we display numerical experiments of cases where MLMC is, and is not, efficient when compared to Monte-Carlo.