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计算数学  2019, Vol. 41 Issue (2): 126-155    DOI:
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高阶分裂步(θ1,θ2,θ3)方法的强收敛性
岳超
郑州航空工业管理学院 经贸学院, 郑州 450015
STRONG CONVERGENCE OF HIGH-ORDER SPLIT-STEP (θ1, θ2, θ3) METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Chao Yue
School of Economics and Trade, Zhengzhou University of Aeronautics, Zhengzhou 450015, China
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摘要 本文首先提出一类高阶分裂步(θ1θ2θ3)方法求解由非交换噪声驱动的非自治随机微分方程.其次在漂移项系数满足多项式增长和单边Lipschitz条件下,证明了当1/2 ≤ θ2 ≤ 1时该方法是1阶强收敛的.此类方法包含很多经典的方法:如随机θ-Milstein方法,向后分裂步Milstein方法等.最后数值实验验证了所得结论.
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关键词随机微分方程   高阶分裂步(&theta   1   &theta   2   &theta   3)方法   强收敛性     
Abstract: In this paper, we first propose high-order split-step (θ1, θ2, θ3) methods for non-autonomous stochastic differential equations (SDEs) driven by non-commutative noise. Then, we prove that for 1/2 ≤ θ2 ≤ 1 the high-order split-step (θ1, θ2, θ3) methods are convergent with strong order of one for SDEs with the drift coefficient satisfying a superlinearly growing condition and a one-sided Lipschitz continuous condition. The high-order split-step (θ1, θ2, θ3) methods contain some classical methods such as stochastic θ-Milstein method, split-step back Milstein method and so on. Finally, the obtained results are verified by numerical experiments.
Key wordsStochastic differential equations   High-order Split-step (θ1, θ2, θ3) methods   Strong convergence   
收稿日期: 2017-04-29; 出版日期: 2019-05-18
基金资助:

国家自然科学基金(11371157,71603243),河南省高校重点科研项目(17A110013,17A520062),2016年河南省政府决策研究招标课题(2016B017,2016B013)和2017年度河南省科技攻关计划(高新技术领域)项目(172102210529)资助.

引用本文:   
. 高阶分裂步(θ1,θ2,θ3)方法的强收敛性[J]. 计算数学, 2019, 41(2): 126-155.
. STRONG CONVERGENCE OF HIGH-ORDER SPLIT-STEP (θ1, θ2, θ3) METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2019, 41(2): 126-155.
 
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