A Semigroup Approach to Nonlinear Lévy Processes

Denk R, Kupper M, Nendel M (2019) Center for Mathematical Economics Working Papers; 610.
Bielefeld: Center for Mathematical Economics.

Diskussionspapier | Veröffentlicht | Englisch
 
Download
OA 455.35 KB
Autor/in
; ;
Abstract / Bemerkung
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 ($A_\lambda$) $_{\lambda\in \Lambda}$ 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 $\partial_t u=\sup_{\lambda\in \Lambda} A_\lambda u$. The results are illustrated with several examples.
Stichworte
Lévy process; convex expectation space; Markovian convolution semigroup; fully nonlinear PDE; Nisio semigroup
Erscheinungsjahr
2019
Band
610
ISSN
0931-6558
Page URI
https://pub.uni-bielefeld.de/record/2934230

Zitieren

Denk R, Kupper M, Nendel M. A Semigroup Approach to Nonlinear Lévy Processes. Center for Mathematical Economics Working Papers. Vol 610. Bielefeld: Center for Mathematical Economics; 2019.
Denk, R., Kupper, M., & Nendel, M. (2019). A Semigroup Approach to Nonlinear Lévy Processes (Center for Mathematical Economics Working Papers, 610). Bielefeld: Center for Mathematical Economics.
Denk, R., Kupper, M., and Nendel, M. (2019). A Semigroup Approach to Nonlinear Lévy Processes. Center for Mathematical Economics Working Papers, 610, Bielefeld: Center for Mathematical Economics.
Denk, R., Kupper, M., & Nendel, M., 2019. A Semigroup Approach to Nonlinear Lévy Processes, Center for Mathematical Economics Working Papers, no.610, Bielefeld: Center for Mathematical Economics.
R. Denk, M. Kupper, and M. Nendel, A Semigroup Approach to Nonlinear Lévy Processes, Center for Mathematical Economics Working Papers, vol. 610, Bielefeld: Center for Mathematical Economics, 2019.
Denk, R., Kupper, M., Nendel, M.: A Semigroup Approach to Nonlinear Lévy Processes. Center for Mathematical Economics Working Papers, 610. Center for Mathematical Economics, Bielefeld (2019).
Denk, Robert, Kupper, Michael, and Nendel, Max. A Semigroup Approach to Nonlinear Lévy Processes. Bielefeld: Center for Mathematical Economics, 2019. Center for Mathematical Economics Working Papers. 610.
Alle Dateien verfügbar unter der/den folgenden Lizenz(en):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Volltext(e)
Access Level
OA Open Access
Zuletzt Hochgeladen
2019-09-06T09:19:06Z
MD5 Prüfsumme
6f84492b6428e71bc479a0ed951e54a2

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Suchen in

Google Scholar