关于一类平均场正倒向随机微分方程的后验估计
A Posteriori Estimate for a Class of Mean-Field Forward-backward Stochastic Differential Equations
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摘要: 本文研究了一类耦合平均场正倒向随机微分方程的数值解法, 在其解耦场存在并满足一定正则性的条件下,给出了正倒向随机微分方程的后验估计.该后验估计表明正倒向方程解的误差可以由终端项的误差所控制, 进一步,我们基于深度神经网络提出了数值算法并对离散格式进行了收敛性分析.Abstract: We study the numerical solutions for a class of coupled mean-field forward-backward stochastic differential equations. Under suitable regularity assumptions, a posteriori estimate of forward-backward stochastic differential equation is provided. This posterior estimate indicates that the error of the solution for the forward-backward equation can be controlled by the error of the terminal term. Furthermore, we propose a numerical algorithm based on deep neural network and conduct convergence analysis on the discretization scheme.