Please use this identifier to cite or link to this item:
Fuhrmann, Sven
Kupper, Michael
Nendel, Max
Year of Publication: 
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 649
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
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 modelled 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 Levy processes, infinite-dimensional Ornstein-Uhlenbeck processes, geometric Brownian motions, and Koopman semigroups.
Wasserstein distance
nonparametric uncertainty
convex semigroup
viscosity solution
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

Files in This Item:

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.