| 求解非线性随机微分方程半隐无导数法的稳定性 |
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| 引用本文： | 王鹏飞,殷凤,蔺小林.求解非线性随机微分方程半隐无导数法的稳定性[J].河北大学学报(自然科学版),2009,29(2):113. |
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| 作者姓名： | 王鹏飞 殷凤 蔺小林 |
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| 作者单位： | 1.忻州师范学院,数学系,山西,忻州,034000;陕西科技大学,理学院,陕西,西安,710021； 2.忻州师范学院,数学系,山西,忻州,034000； 3.陕西科技大学,理学院,陕西,西安,710021 |
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| 基金项目： | 国家自然科学基金，忻州师范学院自然科学基金 |
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| 摘 要： | 研究了半隐无导数法用于求解非线性随机微分方程的稳定性,利用随机变量服从正态分布的性质,得到了在噪声为乘性噪声时,半隐无导数法用于求解标量自治非线性随机微分方程的均方稳定性、指数稳定性和T-稳定性的充分条件.
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| 关 键 词： | 半隐无导数 随机微分方程 均方稳定性 指数稳定性 T-稳定性 |
Stability of the Semi-implicit Derivative-free Methods for Solving Non-linearity Stochastic Differential Equations |
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| WANG Peng-fei,YIN Feng,LIN Xiao-lin.Stability of the Semi-implicit Derivative-free Methods for Solving Non-linearity Stochastic Differential Equations[J].Journal of Hebei University (Natural Science Edition),2009,29(2):113. |
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| Authors: | WANG Peng-fei YIN Feng LIN Xiao-lin |
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| Affiliation: | 1.Department of Mathematics;Xinzhou Teacher' s University;Xinzhou 034000;China;2.Faculty of Science;Shanxi University of Science and Technolgy;Xi'an 710021;China |
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| Abstract: | The stability of the semi-implicit derivative-free method in solving non-linearity 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 the semi-implicit derivative-free method in solving autonomous scalar stochastic non-linearity differential equations was gained by using the property of stochastic variable being subordinated to normal distribution. |
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| Keywords: | semi-implicit derivative-free methods non-linearity stochastic differential equation mean square stability exponential stability T-stability |
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