| 随机微分方程高阶分裂步(θ1,θ2,θ3)方法的强收敛性 |
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| 引用本文： | 岳超.随机微分方程高阶分裂步(θ1,θ2,θ3)方法的强收敛性[J].计算数学,2019,41(2):126-155. |
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| 作者姓名： | 岳超 |
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| 作者单位： | 郑州航空工业管理学院经贸学院,郑州,450015 |
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| 基金项目： | 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. |
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| 摘 要： | 本文首先提出一类高阶分裂步（θ1，θ2，θ3）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(θ1 θ2 θ3)方法 强收敛性 |
| 收稿时间： | 2017-04-29 |
STRONG CONVERGENCE OF HIGH-ORDER SPLIT-STEP (θ1, θ2, θ3) METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS |
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| Chao Yue.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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| Authors: | Chao Yue |
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| Institution: | School of Economics and Trade, Zhengzhou University of Aeronautics, Zhengzhou 450015, China |
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| 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. |
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| Keywords: | Stochastic differential equations High-order Split-step (θ1 θ2 θ3) methods Strong convergence |
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