求解非线性随机延迟微分方程加权格式的收敛性  

Convergence of the Weighted Format for Non-linearity Stochastic Delay Differential Equation

作　　者：王鹏飞[1] 殷凤[1] 

机构地区：[1]忻州师范学院数学系,山西忻州034000

出　　处：《郑州大学学报（理学版）》2011年第1期16-19,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：忻州师范学院自然科学基金资助项目;编号200805

摘　　要：通过研究加权格式用于求解非线性随机微分方程的收敛性,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,加权格式用于求解非线性随机微分方程均值意义上的局部收敛阶为2,均方意义上的局部收敛阶为1,强收敛阶为1.The convergence of the weighted format method in solving non-linearity stochastic delay differential equations was studied.In the circumstance of measurement noise,the convergence of weighted format method in solving non-linearity stochastic delay differential equations was gained.By using the property of stochastic variable being subordinated to normal distribution,the equal local convergence,average local convergence and strong convergence order of weighted format were 2,1 and 1.

关 键 词：随机微分方程 加权格式 收敛阶 全局Lipschitz条件 

分 类 号：O175[理学—数学]