Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/278516
Year of Publication: 
2023
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 680
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not rely on the theory of viscosity solutions but use a recent comparison principle which uniquely determines the semigroup via its Γ-generator defined on the Lipschitz set and therefore resembles the classical analogue from the linear case. The framework also allows for discretizations both in time and space and covers a variety of applications. This includes Euler schemes and Yosida-type approximations for upper envelopes of families of linear semigroups, stability results and finite-difference schemes for convex HJB equations, Freidlin-Wentzell-type results and Markov chain approximations for a class of stochastic optimal control problems and continuous-time Markov processes with uncertain transition probabilities.
Subjects: 
convex monotone semigroup
infinitesimal generator
convergence of semigroups
Euler formula
optimal control
finite-difference scheme
Markov chain approximation
large deviations
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Working Paper

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