Wasserstein Perturbations of Markovian Transition Semigroups

Fuhrmann S, Kupper M, Nendel M (2021) Center for Mathematical Economics Working Papers; 649.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
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Fuhrmann, Sven; Kupper, Michael; Nendel, MaxUniBi
Abstract / Bemerkung
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 Lévy processes, infinite-dimensional Ornstein-Uhlenbeck processes, geometric Brownian motions, and Koopman semigroups.

AMS 2020 Subject Classification: Primary 60J35; 47H20; Scondary 60G65; 90C31; 62G35
Stichworte
Wasserstein distance; nonparametic uncertainty; convex semigroup; nonlinear PDE; viscosity solution
Erscheinungsjahr
2021
Band
649
Seite(n)
33
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2954862

Zitieren

Fuhrmann S, Kupper M, Nendel M. Wasserstein Perturbations of Markovian Transition Semigroups. Center for Mathematical Economics Working Papers. Vol 649. Bielefeld: Center for Mathematical Economics; 2021.
Fuhrmann, S., Kupper, M., & Nendel, M. (2021). Wasserstein Perturbations of Markovian Transition Semigroups (Center for Mathematical Economics Working Papers, 649). Bielefeld: Center for Mathematical Economics.
Fuhrmann, S., Kupper, M., and Nendel, M. (2021). Wasserstein Perturbations of Markovian Transition Semigroups. Center for Mathematical Economics Working Papers, 649, Bielefeld: Center for Mathematical Economics.
Fuhrmann, S., Kupper, M., & Nendel, M., 2021. Wasserstein Perturbations of Markovian Transition Semigroups, Center for Mathematical Economics Working Papers, no.649, Bielefeld: Center for Mathematical Economics.
S. Fuhrmann, M. Kupper, and M. Nendel, Wasserstein Perturbations of Markovian Transition Semigroups, Center for Mathematical Economics Working Papers, vol. 649, Bielefeld: Center for Mathematical Economics, 2021.
Fuhrmann, S., Kupper, M., Nendel, M.: Wasserstein Perturbations of Markovian Transition Semigroups. Center for Mathematical Economics Working Papers, 649. Center for Mathematical Economics, Bielefeld (2021).
Fuhrmann, Sven, Kupper, Michael, and Nendel, Max. Wasserstein Perturbations of Markovian Transition Semigroups. Bielefeld: Center for Mathematical Economics, 2021. Center for Mathematical Economics Working Papers. 649.
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2021-05-18T09:32:02Z
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