论文标题
向后的Euler方法的均方体收敛和稳定性，用于具有高度非线性生长系数的随机微分延迟方程
Mean-square convergence and stability of the backward Euler method for stochastic differential delay equations with highly nonlinear growing coefficients
论文作者
论文摘要
在过去的几十年中，许多学者已经研究和开发了随机差延迟方程（SDDE）的数值方法。但是，仍然几乎没有工作要完成。借助新技术，本文着重于向后欧拉方法（BEM）的均方相互收敛和稳定性，这些SDDES的漂移和扩散系数都可以在多个一级上生长。获得了BEM的上部均方误差边界。然后，在不使用数值溶液的力矩界限的情况下揭示了收敛速率。此外，在相当普遍的条件下，新颖的技术被应用于证明BEM可以以简单的证明继承指数的均方根稳定性。最后，实施了两个数值实验，以说明这些理论的可靠性。
Over the last few decades, the numerical methods for stochastic differential delay equations (SDDEs) have been investigated and developed by many scholars. Nevertheless, there is still little work to be completed. By virtue of the novel technique, this paper focuses on the mean-square convergence and stability of the backward Euler method (BEM) for SDDEs whose drift and diffusion coefficients can both grow polynomially. The upper mean-square error bounds of BEM are obtained. Then the convergence rate, which is one-half, is revealed without using the moment boundedness of numerical solutions. Furthermore, under fairly general conditions, the novel technique is applied to prove that the BEM can inherit the exponential mean-square stability with a simple proof. At last, two numerical experiments are implemented to illustrate the reliability of the theories.
