Convergence of infinitesimal generators and stability of convex monotone semigroups - Jonas Blessing; Michael Kupper; Max Nendel (Bielefeld University, Center for Mathematical Economics (IMW), 2023)
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.
urn:nbn:de:0070-pub-29797309
Keywords: 330; convex monotone semigroup; infinitesimal generator; convergence of semigroups; Euler formula; optimal control; finite-difference scheme; Markov chain approximation; large deviations