非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性  

STRONG CONVERGENCE OF THE ELUER-MARUYAMA METHOD FOR STOCHASTIC FRACTIONAL DELAY INTEGRO-DIFFERENTIAL EQUATIONS

作　　者：王琳[1] 许珊珊 王文强[1] Wang Lin;Xu Shanshan;Wang Wenqiang(Hunan Key Laboratory for Computation and Simulation in Science and Engineering,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学科学工程计算与数值仿真湖南省重点实验室,湘潭411105

出　　处：《计算数学》2023年第1期57-73,共17页Mathematica Numerica Sinica

基　　金：国家自然科学基金(12071403);湖南省教育厅重点项目(18A049)资助。

摘　　要：本文研究了一类新的模型问题:非线性随机分数阶延迟积分微分方程.当方程中的漂移项和扩散项满足全局Lipschitz条件和线性增长条件时,基于压缩映射原理给出了该方程解存在唯一的充分条件.由于理论求解的困难,构造了一种数值方法(Euler-Maruyama方法),并证得强收敛阶为α-1/2,α∈(1/2,1].最后通过数值试验,验证了这一理论结果.This paper studies a new type of model problem:nonlinear stochastic fractional delay integro-differential equations.Under the assumptions that the drift and diffusion terms in the equation satisfy the global Lipschitz condition and linear growth condition,the existence and uniqueness of the solution is proved by using contraction mapping principle.Due to the difficulty of theoretical solution,a numerical method(Euler-Maruyama method)is constructed and the order of strong convergence is proved to beα-1/2,α∈(1/2,1].Finally,the theoretical results are verified by numerical experiments.

关 键 词：随机分数阶延迟积分微分方程 Eluer-Maruyama方法 强收敛性 解的存在唯一性 Caputo分数微分算子 

分 类 号：O211.63[理学—概率论与数理统计]