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Convergence and stability of the two classes of balanced Euler methods for stochastic differential equations with locally Lipschitz coefficients
International Journal of Computer Mathematics ( IF 1.8 ) Pub Date : 2021-09-23 , DOI: 10.1080/00207160.2021.1960984
Rui Li 1 , Wei Zhang 2
Affiliation  

In this paper, we consider stochastic differential equations with locally Lipschitz coefficients. Two classes of balanced Euler method are presented. Their moment boundedness and their convergence are considered. Their convergence rates are shown to be that of the classical Euler method. Moreover, the methods are showed that they can reproduce the mean square exponential stability of SDEs.



中文翻译:

具有局部Lipschitz系数的随机微分方程的两类平衡欧拉方法的收敛性和稳定性

在本文中,我们考虑具有局部 Lipschitz 系数的随机微分方程。提出了两类平衡欧拉方法。考虑了它们的矩有界性和收敛性。它们的收敛速度显示为经典欧拉方法的收敛速度。此外,这些方法表明它们可以重现 SDE 的均方指数稳定性。

更新日期:2021-09-23
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