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arXiv · 2009.04941

Mean-square contractivity of stochastic $\theta$-methods

Raffaele D'Ambrosio·Stefano Di Giovacchino
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Abstract

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.

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Raffaele D'Ambrosio, Stefano Di Giovacchino. 2020-09-10. Mean-square contractivity of stochastic $\theta$-methods. https://doi.org/10.1016/j.cnsns.2020.105671

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