随机微分方程Milstein方法的稳定性  

The stability properties of Milstein scheme for stochastic differential equations

作　　者：朱霞[1] 李建国[1] 李宏智[1] 姜珊珊[1] 

机构地区：[1]华中科技大学数学系

出　　处：《华中科技大学学报（自然科学版）》2003年第3期111-113,共3页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目 ( 699740 1 8) .

摘　　要：基于随机微分方程的两类试验方程 ,即噪声为增加噪声和附加噪声的两种情况 ,讨论了求解标量自治随机微分方程的Milstein数值方法的三种稳定性 :A 稳定性、均方稳定性和T 稳定性 .得出确定性情形的A 稳定性延伸到随机性情形时保持不变的结论 。Based on the two types of test equations of stochastic differential equations, additive noise and multiplicative noise, the stability of Milstein numerical scheme for autonomous scalar stochastic differential equations such as the mean square stability, A stability and T stability was studied. It was shown that an extension of the deterministic A stability property holds. The figures of the mean square stability regions were presented for the case when the test equations have real parameters.

关 键 词：随机微分方程 Milstein数值方法 均方稳定性 A-稳定性 T-稳定性 

分 类 号：O175[理学—数学]