Convergence of Infintesimal Generators and Stability of Convex Montone Semigroups

Jonas Blessing, Michael Kupper and Max Nendel
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Jonas Blessing: Center for Mathematical Economics, Bielefeld University
Michael Kupper: Center for Mathematical Economics, Bielefeld University
Max Nendel: Center for Mathematical Economics, Bielefeld University

No 680, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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.

Keywords: convex monotone semigroup; infinitesimal generator; convergence of semigroups; Euler formula; optimal control; finite-difference scheme; Markov chain approximation; large deviations (search for similar items in EconPapers)
Pages: 53
Date: 2023-06-05
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Citations: View citations in EconPapers (1)

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