非线性中立型时滞随机微分方程数值解的指数稳定性  

Exponential stability of nonlinear neutral delay stochastic differential equation

作　　者：宋美玲 胡良剑[1] SONG Meiling;HU Liangjian(College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学理学院

出　　处：《纺织高校基础科学学报》2019年第4期417-424,共8页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(114710071);上海市自然科学基金(17ZR1401300)

摘　　要：在非线性中立型时滞随机微分方程数值解的指数稳定性问题中,一般是将方程中的漂移项系数和扩散项系数分开设置增长性限制条件。为了降低对每个系数增长的限制,将非线性中立型时滞随机微分方程中的漂移项系数和扩散项系数联合考虑,即将两系数的限制在一个式子中,给出了非线性中立型时滞随机微分方程Euler-Maruyama(EM)方法数值解指数稳定性的一类充分性条件。结果显示,在给定的充分性条件下,对于任意初值,运用EM方法得到的非线性中立型时滞随机微分方程的数值解都是几乎处处渐近指数稳定的。On the exponential stability of numerical solutions of the nonlinear neutral delay stochastic differential equation,the drift term coefficients and the diffusion term coefficients in the equations are generally set to the growth limit conditions separately.In order to reduce the limit on the growth of each coefficients,the diffusion term coefficients and the drift term coefficients in nonlinear neutral delay stochastic differential equations were considered together,that is,limiting the two coefficients in a formula.The sufficient conditions for the exponential stability of the Euler-Maruyama(EM)numerical solution of the nonlinear neutral delay differential equation are given.The results show that for the given sufficiency condition,the EM numerical solution of the nonlinear neutral delay differential equation is exponentially stable for any initial value.

关 键 词：中立型时滞随机微分方程 非线性 EM方法 指数稳定性 漂移系数 扩散系数 

分 类 号：O211.63[理学—概率论与数理统计]