一类非线性的带有变时滞的随机微分方程的数值分析  

Numerical analysis of a class of nonlinear stochastic differential equations with variable delay

作　　者：李燕[1] 吴浩 沙翔 高帅斌 LI Yan;WU Hao;SHA Xiang;GAO Shuaibin(College of Science, Huazhong Agricultural University, Wuhan 430072, China;School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China)

机构地区：[1]华中农业大学理学院,武汉430072 [2]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2021年第6期644-649,共6页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(62076106)。

摘　　要：考虑了一类非线性随机时滞微分方程,漂移项系数和扩散项系数均是超线性增长的,其时滞会随着时间变化而变化.建立了这类方程的截断型θ-EM算法,并得到了数值解的收敛率,最后用一个例子验证了理论结果.A class of nonlinear stochastic delay differential equations are considered.The coefficients of drift term and diffusion term are superlinearly increasing,and the delay term varies with time.The truncatedθ-EM algorithm of the equation is established and the convergence rate of the numerical solution is obtained.Finally,an example is given to verify the theoretical result.

关 键 词：随机时滞微分方程 变时滞 截断型θ-EM算法 强收敛率 

分 类 号：O241.8[理学—计算数学]