# Convergence of infinitesimal generators and stability of convex monotone semigroups

arXiv: https://arxiv.org/abs/2305.18981 · HTML: https://mlsanity.com/paper/2305.18981/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2023.

## Built on by (most cited first, 1 of 1)

- [Neural operators approximate strongly continuous convex monotone semigroups](https://mlsanity.com/paper/2609.02727/) (2026)

## Abstract (arXiv)

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 Gamma-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.