Wasserstein Sensitivity of Risk and Uncertainty Propagation

When propagating uncertainty in the data of differential equations, probability laws describing are typically themselves subject to uncertainty. We present a sensitivity analysis propagation for equations with random inputs perturbations input measures. focus on elliptic diffusion equation coefficient and source term, which measure solution field is shown be Lipschitz-continuous both total variation Wasserstein distance. The result generalizes map any locally Hölder dependence parameters. In addition, these results extend quantities interest as well coherent risk functionals applied evaluate impact their Our based pushforward measures mappings respect distance perturbed distributions. established applied, particular, case lognormal truncation series representations fields.