Titelaufnahme

Titel
Upper envelopes of families of feller semigroups and viscosity solutions to a class of nonlinear cauchy problems / Max Nendel and Michael Röckner
VerfasserNendel, Max ; Röckner, Michael In der Gemeinsamen Normdatei der DNB nachschlagen
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, June 2019
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (27 Seiten)
SerieCenter for Mathematical Economics Working papers ; 618
SchlagwörterCauchy-Anfangswertproblem In Wikipedia suchen nach Cauchy-Anfangswertproblem / Viskositätslösung In Wikipedia suchen nach Viskositätslösung
URNurn:nbn:de:hbz:6:2-121889 Persistent Identifier (URN)
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Upper envelopes of families of feller semigroups and viscosity solutions to a class of nonlinear cauchy problems [0.44 mb]
Zusammenfassung

In this paper we construct the smallest semigroup S that dominates a given family of linear Feller semigroups. The semigroup S will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong continuity properties of the semigroup envelope and show that it is a viscosity solution to a nonlinear abstract Cauchy problem. We derive a condition for the existence of a Markov process under a nonlinear expectation for the case where the state space of the Feller processes is locally compact. The procedure is then applied to numerous examples, in particular nonlinear PDEs that arise from control problems for infinite dimensional Ornstein-Uhlenbeck processes and infinite dimensional Lévy processes.

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