论文标题
随机最大原理,延迟延迟,对过去的一般依赖
Stochastic maximum principle for problems with delay with general dependence on the past
论文作者
论文摘要
我们证明了控制问题的随机最大原理,在状态和控制中延迟状态方程,最终的成本功能也可能取决于过去的轨迹。伴随方程式被证明是一种新形式的线性预期向后随机微分方程(在以下中的腹部),我们证明了一个直接的公式来求解这些方程。
We prove a stochastic maximum principle for a control problem where the state equation is delayed both in the state and in the control, and also the final cost functional may depend on the past trajectories. The adjoint equations turn out to be a new form of linear anticipated backward stochastic differential equations (ABSDEs in the following), and we prove a direct formula to solve these equations.