The truncated Euler-Maruyama method for stochastic differential delay equations

被引：38

作者：

Guo, Qian ^{[1
]}

Mao, Xuerong ^{[1
,2
]}

Yue, Rongxian ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China

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

来源：

NUMERICAL ALGORITHMS | 2018年 / 78卷 / 02期

基金：

上海市自然科学基金;

关键词：

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

D O I：

10.1007/s11075-017-0391-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao (Appl. Math. Comput. 217, 5512-5524 2011), and the theory there showed that the Euler-Maruyama (EM) numerical solutions converge to the true solutions in probability. However, there is so far no result on the strong convergence (namely in L (p) ) of the numerical solutions for the SDDEs under this generalized condition. In this paper, we will use the truncated EM method developed by Mao (J. Comput. Appl. Math. 290, 370-384 2015) to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition.

引用

页码：599 / 624

页数：26

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