广义随机Volterra积分微分方程的截断Euler-Maruyama方法的强收敛性
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摘要：
运用截断Euler-Maruyama(EM)方法研究了广义随机Volterra积分微分方程的强收敛性.首先,在局部Lipschitz条件和Khasminskii型条件下证明了截断EM数值解的p阶矩有界性和强收敛性;其次,在较强的假设条件下讨论了截断EM数值解的收敛率;最后通过数值例子验证理论结果的可行性和有效性.
In this paper,the strong convergence of the numerical solutions for generalized stochastic Volterra integro-differential equations is studied by the truncated Euler-Maruyama(EM)method.Firstly,under local Lipschitz condition and the Khasminskii-type condition,we prove the p th moment boundedness and strong convergence of the truncated EM method of the numerical solutions.Furthermore,under some stronger assumptions,the convergence rate of the truncated EM method of the numerical solutions is discussed.Finally,a numerical example is given to illustrate the feasibility and validity of our theoretical results.
作者：
韦煜明 王艳霞 申芳芳
Wei Yuming;Wang Yanxia;Shen Fangfang(School of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)
机构地区：
广西师范大学数学与统计学院
出处：
《betway官方app 学报：自然科学版》 CAS 北大核心 2022年第1期73-81,共9页
Journal of Henan Normal University(Natural Science Edition)
基金：
广西省科技基地和人才专项(2019AC20186,2018AD19211) 广西师范大学科研育人专项(2020YR001)
关键词：
随机积分微分方程 局部LIPSCHITZ条件 Khasminskii型条件 截断EM方法 强收敛性
stochastic integro-differential equations Locally Lipschitz condition Khasminskii-type condition truncated EM method strong convergence
分类号：
O211.63 [理学—概率论与数理统计]
