NONLINEAR SEMIGROUPS AND LIMIT THEOREMS FOR CONVEX EXPECTATIONS

• 成果类型: Article
• 署名作者: Blessing, Jonas; Kupper, Michael
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Konstanz
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2126
• 发表日期: 2025
• 页码: 779-821
• 关键词: viscosity solutions; large numbers; RISK; extension

摘要

Based on the Chernoff approximation, we provide a general approximation result for convex monotone semigroups which are continuous w.r.t. the mixed topology on suitable spaces of continuous functions. Starting with a family (I (t))t >= 0 of operators, the semigroup is constructed as the limit S(t)f := limn ->infinity I (t/n)n f and is uniquely determined by the time derivative I'(0)f for smooth functions. We identify explicit conditions for the generating family (I (t))t >= 0 that are transferred to the semigroup (S(t))t >= 0 and can easily be verified in applications. Furthermore, there is a structural link between Chernoff type approximations for nonlinear semigroups and law of large numbers and central limit theorem type results for convex expectations. The framework also includes large deviation results.