一类随机微分方程向后欧拉解的指数稳定性

Exponential stability of backward Euler approximations to a class of stochastic differential equations

本文给出随机微分方程向后欧拉逼近解满足指数稳定性的充分条件。通过将线性增长条件改为耗散性条件,改进了已有的结果。此外,构造了一个例子,并通过数值模拟验证了本文的结论。

We provide some sufficient conditions to ensure the exponential stability of backward Euler approximation solutions of stochastic differential equations. We improve the known results by replacing the linear growth condition with the dissipative condition. Moreover,an example is constructed and numerical simulation is carried out to support our conclusion.