B0529
Title: Markovian dynamics under Wasserstein uncertainty
Authors: Max Nendel - Bielefeld University (Germany) [presenting]
Abstract: A class of time-homogeneous continuous-time Markov processes is considered with transition probabilities bearing a nonparametric uncertainty. The uncertainty is modelled by considering perturbations of the transition probabilities within proximity in Wasserstein distance. As a limit over progressively finer time periods, on which the level of uncertainty scales proportionally, we obtain a convex semigroup (family of convex transition operators) satisfying a nonlinear PDE in a viscosity sense. A remarkable observation is that, in standard situations, the nonlinear transition operators arising from nonparametric uncertainty coincide with the ones related to parametric drift uncertainty. On the level of the generator, the uncertainty is reflected as an additive perturbation in terms of a convex functional of first-order derivatives. We additionally provide sensitivity bounds for the convex semigroup relative to the reference model.
