This paper develops the Euler’s polygonal line method for the backward stochastic differential equations (BSDEs) with super-linearly growing generators. The generators are allowed to be super-linearly growing in the first unknown variable $y$ and sub-quadratic growing in the second unknown variable $z$ when the monotonicity condition is satisfied. The convergence rate of the Euler approximation is derived, which also provides a simple proof for the existence of the solution to the monotone BSDEs. The proof is very simple and short, without involving the conventional techniques of truncating and smoothing on the generators.

中文翻译：

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用欧拉多边形线法用超线性增长的发电机逼近BSDE：存在的简单证明

本文针对具有超线性增长生成器的后向随机微分方程（BSDE），开发了Euler折线方法。允许生成器在第一个未知变量中超线性增长$ÿ$ 在第二未知变量中和次二次增长 $ž$当满足单调性条件时。推导了欧拉近似的收敛速度，这也为单调BSDE的解的存在提供了简单的证明。该证明非常简单且简短，没有涉及对生成器进行截断和平滑的常规技术。