带跳的倒向重随机系统的最大值原理及其应用

本文研究带跳的倒向重随机系统的随机控制问题的最优性条件。在控制域为凸且控制变量进入所有系数条件下，分别以局部形式和全局形式给出必要性最优条件和充分性最优条件。把上述最大值原理应用于重随机线性二次最优控制问题，得到唯一的最优控制，并且给出应用的例子。

Maximum principles for backward doubly stochastic systems with jumps and applications

We investigate the optimality conditions for stochastic control problems of backward doubly stochastic systems with jumps. Necessary and sufcient optimality conditions, where the control domains are convex and the control is allowed to enter into all the coefcients, are proved. The results are stated in the local form of stochastic maximum principle, as well as in the global form. Applying the stochastic maximum principles to doubly stochastic linear quadratic control problems, we obtain the unique optimal control. An example is given to illustrate the theoretical results.