The aim of this paper is the analysis of exponential mean-square stability properties of nonlinear stochastic linear multistep methods. In particular it is known that, under certain hypothesis on the drift and diffusion terms of the equation, exponential mean-square contractivity is visible: the qualitative feature of the exact problem is here analysed under the numerical perspective, to understand whether a stochastic linear multistep method can provide an analogous behaviour and which restrictions on the employed stepsize should be imposed in order to reproduce the contractive behaviour. Numerical experiments confirming the theoretical analysis are also given.

中文翻译：

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随机线性多步法的指数均方稳定性性质

本文的目的是分析非线性随机线性多步方法的指数均方稳定性特性。特别是已知，在方程的漂移项和扩散项的某些假设下，指数均方收缩性是可见的：这里从数值角度分析确切问题的定性特征，以了解是否随机线性多步方法可以提供类似的行为，并且应该对所采用的步长施加哪些限制以重现收缩行为。还给出了证实理论分析的数值实验。