计算数学
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计算数学  2019, Vol. 41 Issue (1): 12-36    DOI:
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随机微分方程改进的分裂步单支θ方法的强收敛性
张维, 王文强
湘潭大学科学工程计算与数值仿真湖南省重点实验室, 湘潭 411105
STRONG CONVERGENCE OF THE IMPROVED SPLIT-STEP ONE-LEG θ METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Zhang Wei, Wang Wenqiang
Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China
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摘要 本文提出了一个改进的分裂步单支θ方法,在漂移项系数满足单边Lipschitz条件下,证明了当数值方法的参数θ满足1/2 ≤ θ ≤ 1时,该数值方法对于这类随机微分方程是强收敛的,并在现有文献的基础上将方法的收敛阶从1/2阶提高到1阶;当0 ≤ θ ≤ 1/2时,若漂移项系数进一步满足线性增长条件,该数值方法也是强收敛的,收敛阶为1阶.文末的数值试验验证了理论结果的正确性.
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关键词随机微分方程   单边Lipschitz条件   改进的分裂步单支&theta   方法   强收敛性     
Abstract: In this paper a class of methods, called improved split-step one-leg theta methods(ISSOLTM), are introduced and are shown to be convergent for SDEs with one-sided Lipschitz continuous drift coefficient if the method parameter satisfies 1/2 ≤ θ ≤ 1. At the same time, we improve the strong order from one half to one on the basis of the existing literature. For 0 ≤ θ ≤ 1/2, under the additional linear growth condition for the drift coefficient, the methods are also strongly convergent with the the order 1. Finally, the obtained results are supported by numerical experiments.
Key wordsstochastic differential equation   one-sided Lipschitz condition   improved split-step one-leg theta methods   strong convergence   
收稿日期: 2017-03-18;
基金资助:

国家自然科学基金(11571373,11671343)、湖南省教育厅重点项目.

通讯作者: 王文强,Email:wwq@xtu.edu.cn     E-mail: wwq@xtu.edu.cn
引用本文:   
. 随机微分方程改进的分裂步单支θ方法的强收敛性[J]. 计算数学, 2019, 41(1): 12-36.
. STRONG CONVERGENCE OF THE IMPROVED SPLIT-STEP ONE-LEG θ METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2019, 41(1): 12-36.
 
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