论文标题
ITô的措施流量的公式
Itô's formula for flows of measures on semimartingales
论文作者
论文摘要
我们沿着与一般半明星相关的概率度量的流动建立了ITô公式；这概括了现有的ITô过程措施流量的结果。我们的方法是首先建立ITô的圆柱函数公式，然后通过函数近似和定位技术将其扩展到一般情况。 ITô公式的这种通用形式可以使McKean-vlasov Controls和McKean-vlasov-vlasov混合常规及定向控制问题的动态编程方程和验证定理衍生。它还允许将最大原理和动态编程原理之间的经典关系推广到McKean-Vlasov单数控制设置，在这种情况下，伴随过程是根据概率度量的值函数的导数表示。
We establish Itô's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô's formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques. This general form of Itô's formula enables the derivation of dynamic programming equations and verification theorems for McKean--Vlasov controls with jump diffusions and for McKean--Vlasov mixed regular-singular control problems. It also allows for generalizing the classical relationship between the maximum principle and the dynamic programming principle to the McKean--Vlasov singular control setting, where the adjoint process is expressed in terms of the derivative of the value function with respect to the probability measures.
