The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.

中文翻译：

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随机泛函微分方程的Ulam-Hyers-Rassias稳定性不动点法

许多研究人员已经使用Gronwall型不等式研究了随机系统的Ulam-Hyers-Rassias稳定性，但是没有关于通过固定点方法的随机泛函微分方程的Ulam-Hyers-Rassias稳定性的研究。本文的主要目的是研究随机泛函微分方程（SFDE）的Ulam-Hyers稳定性（HUS）和Ulam-Hyers-Rassias稳定性（HURS）。在定点方法和随机分析技术的基础上，研究了SFDE的稳定性结果。我们分析两个说明性的例子，以显示结果的有效性。