论文标题
非线性半群和限制定理以达到凸期的期望
Nonlinear semigroups and limit theorems for convex expectations
论文作者
论文摘要
基于Chernoff的近似，我们为连续W.R.T.的凸单酮半群提供了一般的近似结果。连续功能的合适空间上的混合拓扑。从一个家庭$（i（t））_ {t \ geq 0} $开始，将半群构造为限制$ s（t）f：= \ lim_ {n \ to \ infty} i（\ frac {t} {n} {n} {n} {n}）^n f $，并且按时间导出$ i'（0）f $'（0）f $'（0）f $'（0）f。我们确定了生成家庭$（i（t））_ {t \ geq 0} $的明确条件，该_ {t \ geq 0} $转移到semigroup $（s（t））_ {t \ geq 0} $，并且可以在应用程序中轻松验证。此外，非线性半群的Chernoff类型近似与大量定律和中央限制定理类型的结果之间存在结构联系。该框架还包括较大的偏差结果。
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 $(I(t))_{t\geq 0}$ of operators, the semigroup is constructed as the limit $S(t)f:=\lim_{n\to\infty}I(\frac{t}{n})^n f$ and is uniquely determined by the time derivative $I'(0)f$ for smooth functions. We identify explicit conditions for the generating family $(I(t))_{t\geq 0}$ that are transferred to the semigroup $(S(t))_{t\geq 0}$ 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.
