| 线性随机微分方程多步法的稳定性 |
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| 引用本文： | 王鹏飞,郭忠海,殷凤,王娜,蔺小林.线性随机微分方程多步法的稳定性[J].数学的实践与认识,2014(1). |
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| 作者姓名： | 王鹏飞 郭忠海 殷凤 王娜 蔺小林 |
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| 作者单位： | 忻州师范学院数学系;河北工业大学理学院;陕西科技大学电气与信息工程学院; |
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| 基金项目： | 国家自然科学基金(NSFC10771168);山西省教育科技开发项目(20121111);忻州师范学院重点建设学科项目 |
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| 摘 要： | 研究了多步法用于求解线性随机微分方程的稳定性,利用维纳过程的增量服从正态分布的性质,得到了在乘性噪声情况下,多步法用于线性随机微分方程的均方稳定性的条件,并用MATLAB对实际算例进行了数值模拟.
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| 关 键 词： | 多步法 随机微分方程 均方稳定 T-稳定性 |
Stability of the Multistep Methods of Linear Stochastic Differential Equations |
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| Abstract: | The positive solutions to the stability of Multi-step method in solving stochastic differential equations are studied.In the circumstance of measurement noise,the sufficient and necessary conditions for the mean square stability,the exponential stability and T stability of Multi-step method in solving autonomous scalar stochastic differential equations was gained by using the property of Wiener process increments being subordinated to normal distribution,numerical experiments are given by MATLAB. |
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| Keywords: | Multistep method stochastic differential equation mean square stability Tstability |
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