Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/201643
Authors: 
Nendel, Max
Röckner, Michael
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 618
Abstract: 
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.
Subjects: 
Nisio semigroup
fully nonlinear PDE
viscosity solution
Feller process
nonlinear expectation
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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