Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems

Max Nendel and Michael Röckner
Additional contact information
Max Nendel: Center for Mathematical Economics, Bielefeld University
Michael Röckner: Center for Mathematical Economics, Bielefeld University

No 618, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: In this paper we construct the smallest semigroup $\mathscr{S}$ that dominates a given family of linear Feller semigroups. The semigroup $\mathscr{S}$ 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.

Keywords: Nisio semigroup; fully nonlinear PDE; viscosity solution; Feller process; nonlinear expectation (search for similar items in EconPapers)
Date: 2019-06-11
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://pub.uni-bielefeld.de/download/2936013/2936014 First Version, 2019 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:618

Access Statistics for this paper

More papers in Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University Contact information at EDIRC.
Bibliographic data for series maintained by Bettina Weingarten ().