论文标题
耦合McKean-Vlasov FBSDE的路径规律性
Path regularity of coupled McKean-Vlasov FBSDEs
论文作者
论文摘要
本文建立了Hölder时间规律性的解决方案，以耦合McKean-Vlasov向前的随机微分方程（MV-FBSDES）。这不仅是基本的数学兴趣，而且对于它们的数值近似也是必不可少的。我们表明，与Lipschitz系数的MV-FBSDE的解决方案三倍，只要它允许Lipschitz解耦场，就可以在$ l^p $ norm中持续1/2-Hölder。特殊示例包括解耦MV-FBSDE，少量时间范围的MV-FBSDES和耦合的随机Pontryagin Systems从平均野外控制问题中进行抗衡。
This paper establishes Hölder time regularity of solutions to coupled McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs). This is not only of fundamental mathematical interest, but also essential for their numerical approximations. We show that a solution triple to a MV-FBSDE with Lipschitz coefficients is 1/2-Hölder continuous in time in the $L^p$-norm provided that it admits a Lipschitz decoupling field. Special examples include decoupled MV-FBSDEs, coupled MV-FBSDEs with a small time horizon and coupled stochastic Pontryagin systems arsing from mean field control problems.
