Theoretical and numerical analysis of the Euler-Maruyama method for generalized stochastic Volterra integro-differential equations

被引：19

作者：

Zhang, Wei ^{[1
]}

Liang, Hui ^{[2
]}

Gao, Jianfang ^{[3
]}

机构：

[1] Heilongjiang Univ, Sch Math Sci, Harbin, Heilongjiang, Peoples R China

[2] Harbin Inst Technol, Sch Sci, Shenzhen, Guangdong, Peoples R China

[3] Harbin Normal Univ, Sch Math Sci, Harbin, Heilongjiang, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 365卷 / 365期

基金：

中国国家自然科学基金;

关键词：

Stochastic Volterra integro-differential equations; Existence and uniqueness; Holder continuity; Euler-Maruyama method; Strong convergence; STRONG-CONVERGENCE; DIFFERENTIAL-EQUATIONS; EXPONENTIAL STABILITY; THETA-METHODS; SIMULATION; RATES; SURE;

D O I：

10.1016/j.cam.2019.112364

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we concern with the theoretical and numerical analysis of the generalized stochastic Volterra integro-differential equations (SVIDEs). The existence, uniqueness, boundedness and Holder continuity of the analytic solutions for generalized SVIDEs are investigated. The Euler-Maruyama method for generalized SVIDEs is presented. The boundedness of the numerical solution is proved, and the strong convergence order is obtained. The theoretical results are illustrated by some numerical examples. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：17

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