• 论文 •

随机延迟微分方程分裂步单支θ方法的强收敛性

1. 湘潭大学数学与计算科学学院, 湘潭 411105
• 收稿日期:2017-06-07 出版日期:2018-06-15 发布日期:2018-06-12
• 基金资助:

国家自然科学基金（11571373，11271311）.

Zhang Wei, Wang Wenqiang. STRONG CONVERGENCE OF THE SPLIT-STEP ONE-LEG θ METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Journal of Numerical Methods and Computer Applications, 2018, 39(2): 135-149.

STRONG CONVERGENCE OF THE SPLIT-STEP ONE-LEG θ METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Zhang Wei, Wang Wenqiang

1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
• Received:2017-06-07 Online:2018-06-15 Published:2018-06-12

This paper establishes the boundedness, convergence of the split-step one-leg theta methods(SSOLTM) for stochastic delay differential equations, When the diffusion obeys the global Lipschitz in both x and y, but the drift f(x, y) satisfies one-sided Lipschitz condition in x and globally Lipschitz in y. In this paper, SSOLTM are shown to be mean-square convergent for such SDDEs if the method parameter satisfies 1/2 ≤ θ ≤ 1. At the same time, we extend the numerical approach from stochastic ordinary differential equations to stochastic delay differential equations on the basis of the existing literature. Finally, the obtained results are supported by numerical experiments.

MR(2010)主题分类:

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