Year: 2026
Type: article
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 recently established comparison principle which uniquely determines semigroups via their upper [Formula: see text]-generator defined on their upper Lipschitz sets and therefore resembles the classical analogue from the linear case. The framework also allows for discretizations in both 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.
DOI: 10.1137/25m1724699
Authors: Jonas Blessing, Michael Kupper, Max Nendel
Institutions: ETH Zurich, University of Konstanz, University of Waterloo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4378945374