论文标题
平均生存力定理和二阶汉密尔顿 - 雅各比方程
Mean viability theorems and second-order Hamilton-Jacobi equations
论文作者
论文摘要
我们介绍了控制随机微分方程的平均生存能力的概念，并建立了Nagumo经典可行性定理的对应物（平均生存能力的必要和充分条件）。作为一种应用，我们提供了比较原理的纯粹概率证明，并且存在二阶完全非线性路径依赖性汉密尔顿 - 雅各布利 - 贝尔曼方程的偶然和粘度解的存在。我们不使用紧凑性和最佳停止参数，这些参数通常用于二阶路径依赖性PDE的文献中。
We introduce the notion of mean viability for controlled stochastic differential equations and establish counterparts of Nagumo's classical viability theorems (necessary and sufficient conditions for mean viability). As an application, we provide a purely probabilistic proof of a comparison principle and of existence for contingent and viscosity solutions of second-order fully nonlinear path-dependent Hamilton-Jacobi-Bellman equations. We do not use compactness and optimal stopping arguments, which are usually employed in the literature on viscosity solutions for second-order path-dependent PDEs.
