The paper is focused on the nonlinear stability analysis of stochastic $\theta$-methods. In particular, we consider nonlinear stochastic differential equations such that the mean-square deviation between two solutions exponentially decays, i.e., a mean-square contractive behaviour is visible along the stochastic dynamics. We aim to make the same property visible also along the numerical dynamics generated by stochastic $\theta$-methods: this issue is translated into sharp stepsize restrictions depending on parameters of the problem, here accurately estimated. A selection of numerical tests confirming the effectiveness of the analysis and its sharpness is also provided.

中文翻译：

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随机$\theta$-方法的均方收缩性

论文的重点是随机$\theta$-方法的非线性稳定性分析。特别地，我们考虑非线性随机微分方程，使得两个解之间的均方偏差呈指数衰减，即沿随机动力学可见均方收缩行为。我们的目标是在随机 $\theta$-methods 生成的数值动力学中也使相同的属性可见：根据问题的参数，这个问题被转化为严格的步长限制，这里是准确估计的。还提供了一系列数值测试，以确认分析的有效性及其清晰度。