线性随机微分方程多步法的稳定性  

Stability of the Multistep Methods of Linear Stochastic Differential Equations

作　　者：王鹏飞[1] 郭忠海[1] 殷凤[1] 王娜[2] 蔺小林[3] 

机构地区：[1]忻州师范学院数学系,山西忻州034000 [2]河北工业大学理学院,天津300401 [3]陕西科技大学电气与信息工程学院,陕西西安710021

出　　处：《数学的实践与认识》2014年第1期269-272,共4页Mathematics in Practice and Theory

基　　金：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

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.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.

关 键 词：多步法 随机微分方程 均方稳定 T-稳定性 

分 类 号：O211.63[理学—概率论与数理统计]