This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation. In addition, the Borel–Cantelli lemma and the stochastic analysis theory are incorporated to discuss the almost sure exponential stability for this numerical solution of such equations.

中文翻译：

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中性随机泛函微分方程数值解的指数稳定性注解

本文研究了中性随机泛函微分方程的数值解。本研究建立了离散随机 Razumikhin 型定理，以研究该方程的 Euler-Maruyama 数值解的均方意义上的指数稳定性。此外，还结合了 Borel-Cantelli 引理和随机分析理论，讨论了此类方程的数值解几乎肯定的指数稳定性。