  In this paper, we deal with a class of time-homogeneous continuous-time
Markov processes with transition probabilities bearing a nonparametric
uncertainty. The uncertainty is modeled by considering perturbations of the
transition probabilities within a 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 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.
The results are illustrated with Wasserstein perturbations of L\'evy processes,
infinite-dimensional Ornstein-Uhlenbeck processes, geometric Brownian motions,
and Koopman semigroups.
