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Analysis of asymptotic mean-square stability of a class of Runge-Kutta schemes for linear systems of stochastic differential equations

机译:一类随机微分方程线性系统Runge-Kutta格式的渐近均方稳定性分析

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In this paper the linear asymptotic mean-square stability of class of diagonally drift-implicit Runge-Kutta schemes (DDISRK) for the weak solution of systems of stochastic differential equations (SDEs) is investigated. We provide explicit structure of the stability matrices of this class of Runge-Kutta schemes for general form of linear systems of SDEs. Then we apply this analysis to several particular linear test SDE systems, that can capture the dynamics of a relatively large subclass of general linear SDE systems, to provide more detailed descriptions of stability properties of DDISRK schemes. Based on this analysis we also propose some optimal parameters that improve asymptotic mean-square stability of some SDE systems with larger drift stiffness. Some comparisons and numerical and illustrative experiments are given that confirm the theoretical discussion.
机译:本文研究了随机微分方程组(SDEs)的弱解的对角漂移隐Runge-Kutta方案(DDISRK)类的线性渐近均方稳定性。我们为SDE线性系统的一般形式提供了此类Runge-Kutta方案稳定性矩阵的显式结构。然后,我们将此分析应用于几个特定的​​线性测试SDE系统,这些系统可以捕获一般线性SDE系统的较大子类的动态,以提供DDISRK方案稳定性特性的更详细描述。基于此分析,我们还提出了一些最佳参数,这些参数可以改善某些具有较大漂移刚度的SDE系统的渐近均方稳定性。进行了一些比较以及数值和例证实验,证实了理论讨论。

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