| 一类具有Markov参数的随机泛函微分方程的指数稳定性 |
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| 引用本文： | 张启敏,周淑霞.一类具有Markov参数的随机泛函微分方程的指数稳定性[J].宁夏大学学报(自然科学版),2005,26(3):193-196,210. |
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| 作者姓名： | 张启敏 周淑霞 |
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| 作者单位： | 1. 宁夏大学,数学计算机学院,宁夏,银川,750021
2. 宁夏大学,学术期刊中心,宁夏,银川,750021 |
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| 基金项目： | 宁夏自然科学基金资助项目（G002）;宁夏高校科研基金资助项目 |
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| 摘 要： | 对Hilbert空间中具有Markov参数的随机泛函微分方程的指数稳定性提出了一种新的判定方法．将这类方程看作若干个随机微分方程，利用非奇异M-矩阵的等价结论给出了一些判定系统指数稳定的充分条件，这是对已有结果的完善和推广．最后，通过一个例子对所得结论进行了说明．
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| 关 键 词： | Markov参数 M-矩阵 指数稳定 鞅 |
| 文章编号： | 0253-2328（2005）03-0193-04 |
| 收稿时间： | 2005-01-17 |
| 修稿时间： | 2005-01-17 |
Exponential Stability of Stochastic Functional Differential Equations with Markovian Jumping Parameters |
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| Zhang Qimin,Zhou Shuxia.Exponential Stability of Stochastic Functional Differential Equations with Markovian Jumping Parameters[J].Journal of Ningxia University(Natural Science Edition),2005,26(3):193-196,210. |
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| Authors: | Zhang Qimin Zhou Shuxia |
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| Institution: | 1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021 ,China; 2. Center of Academic Journal, Ningxia University, Yinchuan 750021, China |
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| Abstract: | A new method is proposed to investigate the exponential stability of stochastic functional differential equations with Markov jumping parameters in Hilbert space. Such an equation can be regarded as the result of several stochastic differential equations switching from one to the others according to the movement of a Markov chain. By using nonsingular M-matrices equivalent statement, a sufficient condition is obtained to ensure the stability. This result is an improvement and extension of the existing results. An example is studied to illustrate the theory. |
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| Keywords: | Markov parameters M-matrix exponential stability martingale |
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