| 中立型随机延迟微分方程分裂步θ方法的强收敛性 |
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| 引用本文： | 彭捷,代新杰,肖爱国,卜玮平.中立型随机延迟微分方程分裂步θ方法的强收敛性[J].计算数学,2020,42(1):18-38. |
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| 作者姓名： | 彭捷 代新杰 肖爱国 卜玮平 |
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| 作者单位： | 湘潭大学数学与计算科学学院, 湘潭 411105 |
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| 基金项目： | 国家自然科学基金（11671343，11601460），湖南省自然科学基金（2018JJ3491）和湖南省研究生科研创新重点项目（CX20190420）资助. |
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| 摘 要： | 中立型随机延迟微分方程常出现在一些科学技术和工程领域中.本文在漂移系数和扩散系数关于非延迟项满足全局Lipschitz条件，关于延迟项满足多项式增长条件以及中立项满足多项式增长条件下，证明了分裂步θ方法对于中立型随机延迟微分方程的强收敛阶为1/2.数值实验也验证了这一理论结果.
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| 关 键 词： | 中立型随机延迟微分方程 分裂步&theta 方法 强收敛 多项式增长 |
| 收稿时间： | 2018-02-08 |
STRONG CONVERGENCE OF THE SPLIT-STEP θ METHOD FOR NEUTRAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS |
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| Peng Jie,Dai Xinjie,Xiao Aiguo,Bu Weiping.STRONG CONVERGENCE OF THE SPLIT-STEP θ METHOD FOR NEUTRAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS[J].Mathematica Numerica Sinica,2020,42(1):18-38. |
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| Authors: | Peng Jie Dai Xinjie Xiao Aiguo Bu Weiping |
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| Institution: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China |
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| Abstract: | Neutral stochastic delay differential equations often appear in some fields of science and engineering. The aim of this article is to investigate the strong convergence of the split-step θ method for neutral stochastic delay differential equations. When the drift and diffusion coefficients satisfy global Lipschitz condition with respect to the present state and the polynomial growth condition about the delay term respectively, and the neutral term may also be polynomial growth, this method is shown to be strongly convergent of order 1/2. Some numerical results are presented to confirm the obtained theoretical results. |
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| Keywords: | Neutral stochastic delay differential equations Split-step θ method Strong convergence Polynomial growth |
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