| 非线性随机延迟微分方程Euler-Maruyama方法的收敛性 |
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| 引用本文： | 王文强,李寿佛,黄山.非线性随机延迟微分方程Euler-Maruyama方法的收敛性[J].系统仿真学报,2007,19(17):3910-3913. |
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| 作者姓名： | 王文强 李寿佛 黄山 |
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| 作者单位： | 湘潭大学数学与计算科学学院,湖南,湘潭,411105 |
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| 基金项目： | 国家自然科学基金;湖南省社会科学基金 |
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| 摘 要： | 首先利用附近已有节点上的值通过插值对延迟项进行数值逼近,这是一种崭新的尝试;然后针对较一般情形下的一类非线性随机延迟微分方程初值问题,得到了带线性插值的Euler-Maruyama方法在均方意义下是收敛的理论结果,它部分推广了已有文献中的相关结论。
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| 关 键 词： | 非线性随机延迟微分方程 Euler-Maruyama方法 插值 收敛性 |
| 文章编号： | 1004-731X（2007）17-3910-04 |
| 收稿时间： | 2006-09-15 |
| 修稿时间： | 2007-01-30 |
Convergence of Euler-Maruyama Methods for Nonlinear Stochastic Delay Differential Equations |
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| WANG Wen-qiang,LI Shou-fu,HUANG Shan.Convergence of Euler-Maruyama Methods for Nonlinear Stochastic Delay Differential Equations[J].Journal of System Simulation,2007,19(17):3910-3913. |
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| Authors: | WANG Wen-qiang LI Shou-fu HUANG Shan |
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| Institution: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China |
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| Abstract: | The error analysis of Euler-Maruyama methods applying to a general class of nonlinear stochastic delay differential equations was concerned with. A new attempt to get the numerical approximation of the delay argument was proposed, i.e, the delay argument was solved by interpolating. It is proved that the Euler-Maruyama methods with linear interpolation procedure is convergent. Moreover, the results can be regarded as a partial extension of the similar conclusions in the present documents. |
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| Keywords: | nonlinear stochastic delay differential equations Euler-Maruyama methods interpolation convergence |
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