论文标题
具有可测量系数的前向后随机微分方程的强溶液
Strong solutions of forward-backward stochastic differential equations with measurable coefficients
论文作者
论文摘要
本文研究了具有不规则系数的前向后随机微分方程（FBSDE）的完全耦合系统的可溶性。特别是，我们假设FBSDE的系数仅是可测量的，并且在正过程中是有限的。我们至关重要的是使用Malliavin微积分理论的紧凑度来构建强溶液。尽管系数的不规则性，但在Malliavin的意义上，解决方案还是可以微分的，并且在Sobolev的意义上是初始变量的功能。
This paper investigates solvability of fully coupled systems of forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.
