摘要翻译：
本文提出了一种新的倒向随机微分方程的数值解法，它起源于傅立叶分析。该方法包括对BSDE进行欧拉时间离散，并用傅立叶变换表示一定的条件期望，然后用快速傅立叶变换(FFT)计算。提出了误差控制问题，并给出了局部误差分析。我们将该方法推广到正倒向随机微分方程（FBSDEs）和反射FBSDEs。数值算例表明了该方法的有效性。
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英文标题：
《A convolution method for numerical solution of backward stochastic
  differential equations》
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作者：
Cody Blaine Hyndman and Polynice Oyono Ngou
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最新提交年份：
2015
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast Fourier transform (FFT). The problem of error control is addressed and a local error analysis is provided. We consider the extension of the method to forward-backward stochastic differential equations (FBSDEs) and reflected FBSDEs. Numerical examples are considered from finance demonstrating the performance of the method.
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PDF链接：
https://arxiv.org/pdf/1304.1783