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 计算数学 2019, Vol. 41 Issue (2): 126-155    DOI:
 论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles 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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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.

 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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