论文标题
McKean-Vlasov具有倾斜亚级别和相关随机控制问题的多价随机微分方程
McKean-Vlasov multivalued stochastic differential equations with oblique subgradients and related stochastic control problems
论文作者
论文摘要
在本文中，我们通过Euler Type和Skorohod的代表理论，证明了McKean-Vlasov多价随机微分方程（简称MVMSDESWOS）的McKean-Vlasov多价随机微分方程的强大解决方案的存在和独特性。对于这种等式，与[19,13]中的方法相比，由于我们无法使用其构成子差异操作员的最大单调属性，因此应用了一些不同的特定技术来解决我们的问题。之后，我们为MVMSDESWOS提供了一个示例，并具有时间依赖性的凸约约束，可以将其简化为MVMSDESWOS。最后，我们考虑一个最佳控制问题，并为价值函数建立动态编程原理。
In this article, we prove the existence of weak solutions as well as the existence and uniqueness of strong solutions for McKean-Vlasov multivalued stochastic differential equations with oblique subgradients (MVMSDEswOS, for short) by means of the equations of Euler type and Skorohod's representation theorem. For this type of equation, compared with the method in [19,13], since we can't use the maximal monotony property of its constituent subdifferential operator, some different specific techniques are applied to solve our problems. Afterwards, we give an example for MVMSDEswOS with time-dependent convex constraints, which can be reduced to MVMSDEswOS. Finally, we consider an optimal control problem and establish the dynamic programming principle for the value function.
