数值计算与计算机应用
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数值计算与计算机应用  2018, Vol. 39 Issue (2): 135-149    DOI:
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随机延迟微分方程分裂步单支θ方法的强收敛性
张维, 王文强
湘潭大学数学与计算科学学院, 湘潭 411105
STRONG CONVERGENCE OF THE SPLIT-STEP ONE-LEG θ METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Zhang Wei, Wang Wenqiang
School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
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摘要 当扩散项系数gx,y)关于变量xy满足全局Lipschitz条件,而漂移项系数fx,y)关于变量x满足单边Lipschitz条件,变量y满足全局Lipschitz条件时,本文建立了随机延迟微分方程分裂步单支θ方法的有界性和收敛性,并证明了当数值方法的参数θ满足1/2≤θ≤1时,分裂步单支θ方法对于这类随机延迟微分方程是强收敛的,并在现有文献的基础上将该方法从随机常微分方程推广到随机延迟微分方程.文末的数值试验验证了理论结果的正确性.
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关键词随机延迟微分方程   分裂步单支&theta   方法   单边Lipschitz条件   强收敛性     
Abstract: 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.
Key wordsstochastic delay differential equations   split-step one-leg theta methods   one-sided Lipschitz condition   strong convergence   
收稿日期: 2017-06-07;
基金资助:

国家自然科学基金(11571373,11271311).

引用本文:   
. 随机延迟微分方程分裂步单支θ方法的强收敛性[J]. 数值计算与计算机应用, 2018, 39(2): 135-149.
. STRONG CONVERGENCE OF THE SPLIT-STEP ONE-LEG θ METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(2): 135-149.
 
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