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Titel
A semigroup approach to nonlinear Lévy processes / Robert Denk, Michael Kupper and Max Nendel
VerfasserDenk, Robert In der Gemeinsamen Normdatei der DNB nachschlagen ; Kupper, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Nendel, Max
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, March 2019
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Elektronische Ressource
Umfang1 Online-Ressource (25 Seiten)
SerieCenter for Mathematical Economics Working papers ; 610
URNurn:nbn:de:hbz:6:2-121800 Persistent Identifier (URN)
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A semigroup approach to nonlinear Lévy processes [0.43 mb]
Zusammenfassung

We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of infinitesimal generators (A) of linear Lévy processes which guarantees the existence of a nonlinear Lévy process such that the corresponding nonlinear Markovian convolution semigroup is a viscosity solution of the fully nonlinear PDE tu=supAu. The results are illustrated with several examples.

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