Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence
Blessing J, Denk R, Kupper M, Nendel M (2022) Center for Mathematical Economics Working Papers; 662.
Bielefeld: Center for Mathematical Economics.
Diskussionspapier
| Veröffentlicht | Englisch
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Autor*in
Blessing, Jonas;
Denk, Robert;
Kupper, Michael;
Nendel, MaxUniBi
Abstract / Bemerkung
We study semigroups of convex monotone operators on spaces
of continuous functions and their behaviour with respect to
$\Gamma$-convergence. In contrast to the linear theory, the domain
of the generator is, in general, not invariant under the semigroup.
To overcome this issue, we consider different versions of invariant
Lipschitz sets which turn out to be suitable domains for weaker
notions of the generator. The so-called $\Gamma$-generator is
defined as the time derivative with respect to $\Gamma$-convergence
in the space of upper semicontinuous functions. Under suitable
assumptions, we show that the $\Gamma$-generator uniquely
characterizes the semigroup and is determined by its evaluation
at smooth functions. Furthermore, we provide Chernoff approximation
results for convex monotone semigroups and show that approximation
schemes based on the same infinitesimal behaviour lead to the same
semigroup. Our results are applied to semigroups related to stochastic
optimal control problems in finite and infinite-dimensional settings as
well as Wasserstein perturbations of transition semigroups.
MSC 2020: Primary 47H20; 47J25; Secondary 35K55; 35B20; 49L20
MSC 2020: Primary 47H20; 47J25; Secondary 35K55; 35B20; 49L20
Stichworte
Convex monotone semigroup;
$\Gamma$--convergence;
Lipschitz set;
comparison principle;
Chernoff approximation;
optimal control;
Wasserstein perturbation
Erscheinungsjahr
2022
Serientitel
Center for Mathematical Economics Working Papers
Band
662
Seite(n)
53
Urheberrecht / Lizenzen
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2961486
Zitieren
Blessing J, Denk R, Kupper M, Nendel M. Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence . Center for Mathematical Economics Working Papers. Vol 662. Bielefeld: Center for Mathematical Economics; 2022.
Blessing, J., Denk, R., Kupper, M., & Nendel, M. (2022). Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence (Center for Mathematical Economics Working Papers, 662). Bielefeld: Center for Mathematical Economics.
Blessing, Jonas, Denk, Robert, Kupper, Michael, and Nendel, Max. 2022. Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence . Vol. 662. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.
Blessing, J., Denk, R., Kupper, M., and Nendel, M. (2022). Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence . Center for Mathematical Economics Working Papers, 662, Bielefeld: Center for Mathematical Economics.
Blessing, J., et al., 2022. Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence , Center for Mathematical Economics Working Papers, no.662, Bielefeld: Center for Mathematical Economics.
J. Blessing, et al., Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence , Center for Mathematical Economics Working Papers, vol. 662, Bielefeld: Center for Mathematical Economics, 2022.
Blessing, J., Denk, R., Kupper, M., Nendel, M.: Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence . Center for Mathematical Economics Working Papers, 662. Center for Mathematical Economics, Bielefeld (2022).
Blessing, Jonas, Denk, Robert, Kupper, Michael, and Nendel, Max. Convex Monotone Semigroups and their Generators with Respect to $\Gamma$-Convergence . Bielefeld: Center for Mathematical Economics, 2022. Center for Mathematical Economics Working Papers. 662.
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