ADVANCES IN THE TRUNCATED EULER-MARUYAMA METHOD FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS

被引：7

作者：

Fei, Weiyin ^{[1
]}

Hu, Liangjian ^{[2
]}

Mao, Xuerong ^{[3
]}

Xia, Dengfeng ^{[4
]}

机构：

[1] Anhui Polytech Univ, Sch Math & Phys, Minist Educ, Key Lab Adv Percept & Intelligent Control High En, Wuhu 241000, Anhui, Peoples R China

[2] Donghua Univ, Dept Appl Math, Shanghai 201620, Peoples R China

[3] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[4] Anhui Polytech Univ, Sch Math & Phys, Wuhu 241000, Anhui, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 04期

基金：

英国工程与自然科学研究理事会; 上海市自然科学基金; 中国国家自然科学基金;

关键词：

Brownian motion; stochastic differential delay equation; Ito's formula; truncated Euler-Maruyama; Khasminskii-type condition; NUMERICAL-SOLUTIONS; THEOREMS;

D O I：

10.3934/cpaa.2020092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Guo et al. [8] are the first to study the strong convergence of the explicit numerical method for the highly nonlinear stochastic differential delay equations (SDDEs) under the generalised Khasminskii-type condition. The method used there is the truncated Euler-Maruyama (EM) method. In this paper we will point out that a main condition imposed in [8] is somehow restrictive in the sense that the condition could force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is then to establish the convergence rate without this restriction.

引用

页码：2081 / 2100

页数：20

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