| 非全局Lipschitz条件下随机延迟微分方程Euler方法的收敛性 |
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| 引用本文： | 范振成,宋明辉.非全局Lipschitz条件下随机延迟微分方程Euler方法的收敛性[J].计算数学,2011,33(4):337-344. |
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| 作者姓名： | 范振成 宋明辉 |
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| 作者单位： | 1. 闽江学院数学系, 福州 350108;
2. 哈尔滨工业大学数学系, 哈尔滨 150001 |
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| 基金项目： | 国家自然科学基金项目，福建省自然科学基金计划项目，福建省教育厅科技项目 |
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| 摘 要： | 大多数随机延迟微分方程数值解的结果是在全局Lipschitz条件下获得的.许多延迟方程不满足全局Lipschitz条件,研究非全局Lipschitz条件下的数值解的性质,具有重要的意义.本文证明了漂移系数满足单边Lipschitz条件和多项式增长条件,扩散系数满足全局Lipschitz条件的一类随机延迟微分方程的Eul...
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| 关 键 词： | 随机延迟微分方程 Euler方法 单边Lipschitz条件 多项式增长条件 |
| 收稿时间： | 2009-09-24; |
CONVERGENCE OF EULER METHODS FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS UNDER NON-GLOBAL LIPSCHITZ CONDITIONS |
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| Fan Zhencheng,Song Minghui.CONVERGENCE OF EULER METHODS FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS UNDER NON-GLOBAL LIPSCHITZ CONDITIONS[J].Mathematica Numerica Sinica,2011,33(4):337-344. |
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| Authors: | Fan Zhencheng Song Minghui |
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| Institution: | 1. Department of Mathematics, Minjiang University, Fuzhou 350108, China;
2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
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| Abstract: | Most of the existing results on the numerical solutions for the stochastic delay differential equations (SDDEs) are proved under the global Lipschitz conditions. However, there are many SDDEs that don't satisfy the global Lipschitz conditions. It is interesting to study the property of the numerical solutions for the SDDEs under the non-global Lipschitz conditions. In this paper, we prove that the Euler methods for SDDEs converge with the order (1/2) when the drift coefficient function satisfies the one-sided Lipschitz conditions and the polynomial growth conditions and the diffusion coefficient function satisfies the global Lipschitz conditions. |
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| Keywords: | Stochastic delay differential equations Euler methods One-sided Lipschitz conditions Polynomial growth conditions |
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