Switching Games of Stochastic Differential Systems
Switching Games of Stochastic Differential Systems
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DOI：
10.1137/050642204
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
Shanjian Tang;S. Hou
中科院分区：
文献类型：
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作者：
Shanjian Tang;S. Hou
针对一般随机微分系统制定了两人零和切换博弈，并使用组合动态规划和粘度求解方法进行了研究。证明了游戏价值的存在。为了证明下值函数和上值函数的相关动态规划原理（DDP），也遇到了与 Fleming 和 Souganidis 的论文中提到的同类的可测量性问题，我们可以通过对其技术的巧妙调整来解决这个问题。此外，传统的直接方法证明下值函数和上值函数的时间连续性也带来了严重的可测性问题。为了解决新的困难，开发了一种微妙的动态规划参数来获得时间连续性，反过来，该参数又用于从具有确定性中间时间的 DDP 导出随机中间时间的 DDP。
A two-player, zero-sum, switching game is formulated for general stochastic differential systems and is studied using a combined dynamic programming and viscosity solution approach. The existence of the game value is proved. For the proof of the related dynamic programming principle (DDP) for the lower and upper value functions, the measurability problem, of the same kind as mentioned in the paper of Fleming and Souganidis, is also encountered, and we are able to get around it via a delicate adaptation of their technique. Moreover, the traditional direct method to prove the time continuity of lower and upper value functions also gives rise to a serious measurability problem. To get around the new difficulty, a subtle dynamic programming argument is developed to obtain the time continuity, which in return is used to derive the DDP for random intermediate times from the DDP with deterministic intermediate times.