随机延迟积分微分方程θ-方法的指数均方稳定性  

Exponential mean square stability of theta approximations for stochastic delay integro-differential equations

作　　者：滕灵芝 张浩敏[1,2] 梁丽芳 TENG Ling-zhi;ZHANG Hao-min;LIANG Li-fang(College of Science,Guilin University of Technology,Guilin 541006,China;School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]桂林理工大学理学院,广西桂林541006 [2]湘潭大学数学与计算科学院,湖南湘潭411105

出　　处：《桂林理工大学学报》2018年第3期585-592,共8页Journal of Guilin University of Technology

基　　金：国家自然科学基金项目(11101101; 61763008; 71762008);广西科技计划项目(2016GXNSFAA380194)

摘　　要：研究了线性随机延迟积分微分方程的数值稳定性,建立了分裂θ-方法和随机线性θ-方法求解线性随机延迟积分微分方程并讨论其稳定性。当θ∈[0,1/2]时,对于步长和漂移系数在一定的限制条件下,两类θ-方法是均方指数稳定的,而对于θ∈(1/2,1],这两类数值格式的指数均方稳定性是没有限制条件的。The numerical stability of linear stochastic delay integro-differential equations(SDIDEs)is studied.Split-step theta(SST)scheme and the stochastic linear theta(SLT)method are used to solve linear SDIDEs and to discuss its stability.It is proved that the two classes of theta methods withθ∈[0,1/2]can recover the exponential mean square stability when some restrictive conditions on stepsize and the drift coefficient are imposed,but forθ∈(1/2,1],these two classes of numerical schemes can reproduce the exponential mean square stability unconditionally.

关 键 词：随机延迟积分微分方程 分裂θ-方法 随机线性θ-方法 指数均方稳定性 

分 类 号：O211.6[理学—概率论与数理统计]