Stabilized explicit methods are particularly efficient for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they loose their efficiency when a severe stiffness is induced by very few "fast" degrees of freedom, as the stiff and nonstiff terms are evaluated concurrently. Therefore, inspired by [A. Abdulle, M. J. Grote, and G. Rosilho de Souza, Preprint (2020), arXiv:2006.00744] we introduce a stochastic modified equation whose stiffness depends solely on the "slow" terms. By integrating this modified equation with a stabilized explicit scheme we devise a multirate method which overcomes the bottleneck caused by a few severely stiff terms and recovers the efficiency of stabilized schemes for large systems of nonlinear SDEs. The scheme is not based on any scale separation assumption of the SDE and therefore it is employable for problems stemming from the spatial discretization of stochastic parabolic partial differential equations on locally refined grids. The multirate scheme has strong order 1/2, weak order 1 and its stability is proved on a model problem. Numerical experiments confirm the efficiency and accuracy of the scheme.

翻译：稳定明确的方法对于大型硬随机差异方程式(SDEs)来说特别有效,因为它们具有广泛的稳定性域。然而,当严格僵硬性是由极少数“快”自由度引发的,因为硬性和非硬性条件同时被评估。因此,受[A.Abdulle、M.J.Grote和G.Rosilho de Souza,Preprint (202020年),arxiv:2006.00744]的启发,我们引入了一个经调整的软性方程式,其僵硬性完全取决于“低”条件。通过将这一经修改的方程式与稳定的明确方案相结合,我们设计了一种多率方法,克服少数严格条件造成的瓶颈,并恢复了非线性SDE大型系统稳定计划的效率。这个方法不是基于SDE的任何规模分离假设(SDE),因此,它可用于应对当地改良电网的随机偏差部分偏差方方程式的空间离析产生的问题。多率方案具有强的顺序1/2、弱性顺序1,其稳定性的实验方案在模型上证明了稳定性。