标题： 关于区域上一致非退化随机微分博弈的动态规划原理 显示英文标题

标题： On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains

摘要： 我们证明了在时间均匀扩散过程的框架下，对于一致非退化随机微分博弈，动态规划原理成立，这里的扩散过程考虑到了首次离开某个区域的时间。零阶“系数”和“自由”项仅仅被假设为可测的。与之前为常停止时间建立的结果不同，我们允许任意停止时间和随机化的停止时间。主要假设是存在一个足够正则的Isaacs方程解，在后续的文章中将移除这一假设。 显示英文摘要

摘要： We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order "coefficient" and the "free" term are only assumed to be measurable. In contrast with previous results established for constant stopping times we allow arbitrary stopping times and randomized ones as well. The main assumption, which will be removed in a subsequent article, is that there exists a sufficiently regular solution of the Isaacs equation.