论文标题
具有粗糙漂移的二次前向后SDE的可不同性
Differentiability of quadratic forward-backward SDEs with rough drift
论文作者
论文摘要
在本文中，我们考虑二次向前的SDES（QFBSDE），因为{}向前方程中的漂移无法满足全球标准的Lipschitz条件，并且是向后系统的驱动程序{laveeres} type $ f（| y | y | y | y | y | y |）| z |^2，$ f $的非线性。我们证明了QFBSDE的Malliavin和经典导数，并提供了这些过程的表示。我们从\ cite {imkdosreis}的意义上研究了该系统的数值近似值，其中作者认为漂移是Lipschitz，而BSDE的驱动程序在传统意义上是二次的（即$ f $是一个正常数）。我们表明，收敛速率与\ cite {imkdosreis}中的收敛速度相同
In this paper, we consider quadratic forward-backward SDEs (QFBSDEs), for {which} the drift in the forward equation does not satisfy the standard globally Lipschitz condition and the driver of the backward system {possesses} nonlinearity of type $f(|y|)|z|^2,$ where $f$ is any locally integrable function. We prove both the Malliavin and classical derivative of the QFBSDE and provide representations of these processes. We study a numerical approximation of this system in the sense of \cite{ImkDosReis} in which the authors assume that the drift is Lipschitz and the driver of the BSDE is quadratic in the traditional sense (i.e., $f$ is a positive constant). We show that the rate of convergence is the same as in \cite{ImkDosReis}
