SIAM Journal on Mathematical Analysis· 2026Q1
Convergence of Infinitesimal Generators and Stability of Convex Monotone Semigroups
- 2citations
- Q1SCImago
- 2026year
Short summary
A new stability result for convex monotone semigroups on continuous functions is established by leveraging the convergence of their infinitesimal generators in a mixed topology, bypassing the need for viscosity solutions.
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Key points
- Provides a stability result for convex monotone semigroups on continuous functions.
- Uses convergence of infinitesimal generators in a mixed topology as the core mechanism.
- Avoids viscosity solutions by employing a new comparison principle.
- Framework accommodates time and space discretizations.
- Applicable to various problems including HJB equations and stochastic optimal control.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. SIAM Journal on Mathematical Analysis, 2026 · DOI ↗
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