| 求解随机微分方程的欧拉法的收敛性 |
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| 引用本文： | 朱霞.求解随机微分方程的欧拉法的收敛性[J].华中科技大学学报(自然科学版),2003,31(3):114-116. |
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| 作者姓名： | 朱霞 |
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| 作者单位： | 华中科技大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目 ( 699740 1 8) . |
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| 摘 要： | 对于求解随机微分方程的数值方法，给出了衡量其有效性的标准之一即强收敛性．证明了欧拉法用于求解标量自治随机微分方程时，在方程的偏移系数和扩散系数均满足线性增长条件和全局李普希兹条件的情形下，当噪声为增加噪声和附加噪声时，欧拉法的收敛阶分别为0．5和1．0．
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| 关 键 词： | 随机微分方程 欧拉法 强收敛阶 线性增长条件 全局李普希兹条件 |
| 文章编号： | 1671-4512(2003)03-0114-03 |
| 修稿时间： | 2002年6月21日 |
Convergence of the Euler scheme for stochastic differential equation |
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| Zhu Xia Zhu Xia Postgraduate, Dept. of Math. Huazhong Univ. of Sci. & Tech.,Wuhan ,China..Convergence of the Euler scheme for stochastic differential equation[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2003,31(3):114-116. |
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| Authors: | Zhu Xia Zhu Xia Postgraduate Dept of Math Huazhong Univ of Sci & Tech Wuhan China |
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| Institution: | Zhu Xia Zhu Xia Postgraduate, Dept. of Math. Huazhong Univ. of Sci. & Tech.,Wuhan 430074,China. |
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| Abstract: | In designing numerical schemes for solving stochastic differential equations, the definition of strong convergence was given. It was one of the criteria to measure the efficiency of a numerical scheme. When Euler scheme was used to solve the scalar autonomous stochastic differential equations and both of the drift coefficient and diffusion coefficient satisfied the linear growth condition and global Lipschitz condition, it was shown that the convergence order of Euler was 0.5 and 1. |
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| Keywords: | stochastic differential equations Euler scheme strong convergence order linear growth condition global Lipschitz condition |
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