• 论文 •

### 高阶分裂步(θ1,θ2,θ3)方法的强收敛性

1. 郑州航空工业管理学院 经贸学院, 郑州 450015
• 收稿日期:2017-04-29 出版日期:2019-06-15 发布日期: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.

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.

### STRONG CONVERGENCE OF HIGH-ORDER SPLIT-STEP (θ1, θ2, θ3) METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Chao Yue

1. School of Economics and Trade, Zhengzhou University of Aeronautics, Zhengzhou 450015, China
• Received:2017-04-29 Online:2019-06-15 Published:2019-05-18

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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