| 分段连续型随机微分方程的均方稳定性分析 |
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| 引用本文： | 戴红玉,刘明珠.分段连续型随机微分方程的均方稳定性分析[J].黑龙江大学自然科学学报,2008,25(5). |
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| 作者姓名： | 戴红玉 刘明珠 |
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| 摘 要： | 考虑了自变量分段连续型随机微分方程(dX(t)=(a1X(t) a2X(t]))dt (61X(t) b2X(t]))dW(t)的解析解和数值解的均方稳定性.得到了解析解的表达形式,证明了当2a1 b2 b21 b222|a2 b1b2<0时,解析解是均方稳定的.在此条件下,讨论了由半隐式欧拉方法得到的数值解的稳定性,得到如下结论:当0≤θ
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| 关 键 词： | 随机微分方程 自变量分段连续型微分方程 随机混杂系统 均方稳定 |
Mean square stability of stochastic differential equations with piecewise continuous arguments |
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| Dai Hongyu,Liu Mingzhu.Mean square stability of stochastic differential equations with piecewise continuous arguments[J].Journal of Natural Science of Heilongjiang University,2008,25(5). |
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| Authors: | Dai Hongyu Liu Mingzhu |
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| Abstract: | The mean-square stability of the analytic and numerical solutions of linear stochastic differential equations dX(t) = (a1X(t) +a2X( t] ) )dt + (b1X(t)+b2X(t] ) )dW(t) with piecewise continuous arguments is investigated. The explicit form of the analytic solutions is obtained, and it is proved that under the condition 2a1 + b21 + b22 + 2|a2 + b1 b2| < 0, the analytic solutions are mean-square stable.The semi-implicit Euler method is defined, and the mean-sqaure stability of the numerical solutions is discussed under the condition. The result is when 0≤θ< (a1-|a2| )2a1, 0
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| Keywords: | SDE EPCA Stochastic hybrid systems MS-stable |
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