随机Perron方法与零和微分对策的初等策略
Stochastic Perron's method and elementary strategies for zero-sum differential games
摘要：
本文在两人零和微分对策的框架下发展了随机Perron方法。我们认为制定的游戏，双方球员发挥，对称，反馈策略（如[CR 09]或[PZ 12]），而不是在文献中流行的埃利奥特-卡尔顿制定。我们使用的反馈策略类是精心选择的，使状态方程承认强解和随机Perron方法中所涉及的技术性问题以一种相当简单的方式进行。更准确地说，我们定义了基本策略上的博弈，这些策略很好地受到直觉的激励。在这个框架内，随机Perron方法产生的粘性子解的上Isaacs方程占主导地位的游戏的上限值，和粘性的上Isaacs方程低于游戏的上限值的超解。利用粘性比较结果，我们得到了上值是Isaacs方程的唯一连续的黏性解。同样的陈述适用于较低值和较低的Isaacs方程。一个版本的动态规划原则获得的副产品。如果Isaacs条件成立，博弈在初等（纯）策略上有一个值。
英文摘要：
We develop here the Stochastic Perron Method in the framework of two-player zero-sum differential games. We consider the formulation of the game where both players play, symmetrically, feed-back strategies (as in [CR09] or [PZ12]) as opposed to the Elliott-Kalton formulation prevalent in the literature. The class of feed-back strategies we use is carefully chosen so that the state equation admits strong solutions and the technicalities involved in the Stochastic Perron Method carry through in a rather simple way. More precisely, we define the game over elementary strategies, which are well motivated by intuition. Within this framework, the Stochastic Perron Method produces a viscosity sub-solution of the upper Isaacs equation dominating the upper value of the game, and a viscosity super-solution of the upper Isaacs equation lying below the upper value of the game. Using a viscosity comparison result we obtain that the upper value is the unique and continuous viscosity solution of the upper Isaacs equation. An identical statement holds for the lower value and lower Isaacs equation. A version of the Dynamic Programming Principle is obtained as a by-product. If the Isaacs condition holds, the game has a value over elementary (pure) strategies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
