发表机构
Seoul National University; University of Freiburg（首尔大学; 弗赖堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在带杀灭的马尔可夫框架下，通过稳健估值、全局化和局部化三个映射，建立了次线性估值与不确定性结构之间的序同构，并给出了局部规范生成的次线性估值的PDE刻画及唯一表示，为模型恢复提供了统一框架。
AI 中文摘要
本文研究在带杀灭的时间齐次马尔可夫框架下，次线性估值规则、不确定性结构和局部规范之间的关系。在上级生成元的有限性和局部性以及李雅普诺夫条件下，这些对象通过三个映射联系起来：稳健估值、全局化和局部化。首先，我们证明相应类别的不确定性结构和次线性估值规则通过稳健估值映射是序同构的。其次，我们的分析阐明了局部规范如何约束次线性估值和不确定性结构，以及局部化和全局化保留哪些信息。特别是，局部化和全局化的复合不一定恢复原始对象，而是产生典型的极值元素。第三，由局部规范生成的次线性估值通过相关的Hamilton--Jacobi--Bellman方程的最大粘性下解来刻画。最后，每个带杀灭的不确定性结构都通过一族由累积贴现过程和底层状态定律组成的对来唯一表示。这些结果为次线性估值中的序关系、概率和PDE表示以及模型恢复提供了框架，而无需底层鞅问题的唯一性或粘性比较原理。
英文摘要
This work studies the relationships among sublinear valuation rules, uncertainty structures, and local specifications in a time-homogeneous Markovian framework with killing. These objects are linked, under finiteness and locality of the upper generator and a Lyapunov condition, by three maps: robust valuation, globalization, and localization. First, we show that the corresponding classes of uncertainty structures and sublinear valuation rules are order-isomorphic via the robust valuation map. Second, our analysis clarifies how local specifications constrain sublinear valuation and uncertainty structures, as well as what information localization and globalization preserve. In particular, the compositions of localization and globalization need not recover the original objects but yield canonical extremal elements. Third, the sublinear valuation generated by a local specification is characterized by the greatest viscosity subsolution of the associated Hamilton--Jacobi--Bellman equation. Finally, each uncertainty structure with killing admits a unique representation by a family of pairs consisting of a cumulative discounting process and an underlying state law. These results provide a framework for order relations, probabilistic and PDE-based representations, and model recovery in sublinear valuation without requiring uniqueness of the underlying martingale problems or a viscosity comparison principle.
