线性随机变延迟微分方程数值解的均方稳定性  

MEAN-SQUARE STABILITY OF NUMERICAL SOLUTIONS FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH VARIABLEDELAY

作　　者：包学忠 胡琳[2] 张思晴 Bao Xuezhong;Hu Lin;Zhang Siqing(College of Artificial Intelligence,Gansu University of Political Science and Law,Lanzhou 730070;College of science,Jiangxi University of Science and Technology,Ganzhou 341000)

机构地区：[1]甘肃政法大学人工智能学院,兰州730070 [2]江西理工大学理学院,赣州341000

出　　处：《高等学校计算数学学报》2023年第4期303-312,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11801238,11561028);江西省教育厅青年资金项目(GJJ170566);江西理工大学创新创业训练计划项目(DC2018-071).

摘　　要：1引言。在现实生活中,某些动力系统不仅依赖于当前状态,而且还会受到各种随机因素的干扰,这类随机系统可以用随机微分方程(SDEs)来描述.如,随机Lotka-Volterra模型(文献[1])、股票价格模型(文献[2])等;然而,在许多实际问题中,事物的变化过程不仅仅取决于事物当前时刻的状态,还取决于过去某个时刻的状态,这种现象在自然界中广泛存在.如,传染病的潜伏期、信号传递和电力传动的时延等.In this paper,a class of split-step method is introduced for linear stochastic variable delay differential equations.In particular,this kind of split-step method includes classical Euler method and split-step backward Euler method.In this article,the step-size range of split-step method to keep the mean-square stability of analytical solution is given and proved.Finally,the correctness of the theoretical results is verified by numerical experiments.

关 键 词：随机微分方程 均方稳定性 线性随机 变延迟微分方程 数值解 随机系统 电力传动 信号传递 

分 类 号：O241.81[理学—计算数学]