论文标题
定向链随机微分方程的平滑度
Smoothness of Directed Chain Stochastic Differential Equations
论文作者
论文摘要
我们研究了定向链随机微分方程的溶液的平滑度，其中每个过程都受到Detring等人的无限为定向链图的邻域过程的影响。 （2020）。由于链式结构的辅助过程，Malliavin衍生物的经典方法不适用。也就是说，我们无法在Malliavin衍生物与状态过程的一阶导数之间建立联系。事实证明，可以在此处使用部分Malliavin衍生物来解决此问题。
We study the smoothness of the solution of the directed chain stochastic differential equations, where each process is affected by its neighborhood process in an infinite directed chain graph, introduced by Detering et al. (2020). Because of the auxiliary process in the chain-like structure, classic methods of Malliavin derivatives are not directly applicable. Namely, we cannot make a connection between the Malliavin derivative and the first order derivative of the state process. It turns out that the partial Malliavin derivatives can be used here to fix this problem.
