| 随机微分方程改进半隐Milstein方法的稳定性 |
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| 引用本文： | 李启勇.随机微分方程改进半隐Milstein方法的稳定性[J].怀化师专学报,2012(5):1-6. |
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| 作者姓名： | 李启勇 |
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| 作者单位： | 怀化学院数学系,湖南怀化418008 |
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| 基金项目： | 湖南省教育厅青年项目（118095）. |
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| 摘 要： | 研究了随机微分方程改进的半隐Milstein方法的均方稳定和渐近稳定性．对线性检验方程，得到了改进的半隐Milstein方法对任意步长△≠〉0均方稳定的充要条件是3/4 ≤ θ ≤ 1．证明了当方法的步长充分小时，方法能保持原系统的渐近稳定性．
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| 关 键 词： | 半隐Milstein方法 随机微分方程 均方稳定 渐近稳定 |
Stability of Improved Semi- implicit Milstein Methods for Stochastic Differential Equations |
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| Institution: | LI Qi - yong ( Department of Mathematics, Huaihua University, Huaihua, Hunan 418008) |
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| Abstract: | This paper gives investigation of mean - square and asymptotic stability of improved semi - implicit Milstein methods for stochastic differential equations. It is shown that the improved semi - implicit Milstein methods recovered the mean- square stability properties of the linear test equation, if and only if 3/4 ≤ θ ≤ 1. For asymptotic stability, we proved that the methods can reproduce the stability of the test problem provided that the stepsize is sufficiently small. |
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| Keywords: | semi- implicit Milstein methods stochastic differential equations mean square stability asymptoticstability |
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