The paper provides a nonlinear stability analysis for a class of stochastic Runge-Kutta methods, applied to problems generating mean-square contractive solutions. In particular, we show how this property is inherited along the solutions generated by the stochastic perturbation of an algebraically stable deterministic Runge-Kutta method. The effectiveness of the results is also confirmed by selected numerical experiments.

中文翻译：

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随机Runge-Kutta方法的非线性稳定性问题

本文提供了一类随机Runge-Kutta方法的非线性稳定性分析，该方法适用于生成均方收缩解的问题。特别是，我们展示了如何通过代数稳定确定性Runge-Kutta方法的随机扰动生成的解继承该属性。结果的有效性也通过选定的数值实验得到证实。