Advances in the truncated Euler-Maruyama method for stochastic differential delay equations

Weiyin Fei, Liangjian Hu, Xuerong Mao, Dengfeng Xia

Research output: Contribution to journalArticle

Abstract

Guo et al. [GMY17] 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 [GMY17] 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.
Original languageEnglish
Pages (from-to)2081-2100
Number of pages20
JournalCommunications on Pure and Applied Analysis
Volume19
Issue number4
DOIs
Publication statusAccepted/In press - 30 Dec 2019

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Euler-Maruyama Method
Stochastic Differential Delay Equations
Numerical methods
Explicit Methods
Strong Convergence
Convergence Rate
Numerical Methods
Restriction

Keywords

  • Brownian motion
  • stochastic differential delay equation
  • truncated Euler-Maruyama
  • Khasminskii-type condition

Cite this

Fei, W., Hu, L., Mao, X., & Xia, D. (Accepted/In press). Advances in the truncated Euler-Maruyama method for stochastic differential delay equations. Communications on Pure and Applied Analysis, 19(4), 2081-2100. https://doi.org/10.3934/cpaa.2020092
Fei, Weiyin ; Hu, Liangjian ; Mao, Xuerong ; Xia, Dengfeng. / Advances in the truncated Euler-Maruyama method for stochastic differential delay equations. In: Communications on Pure and Applied Analysis. 2020 ; Vol. 19, No. 4. pp. 2081-2100.
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Fei, W, Hu, L, Mao, X & Xia, D 2020, 'Advances in the truncated Euler-Maruyama method for stochastic differential delay equations', Communications on Pure and Applied Analysis, vol. 19, no. 4, pp. 2081-2100. https://doi.org/10.3934/cpaa.2020092

Advances in the truncated Euler-Maruyama method for stochastic differential delay equations. / Fei, Weiyin; Hu, Liangjian; Mao, Xuerong; Xia, Dengfeng.

In: Communications on Pure and Applied Analysis, Vol. 19, No. 4, 30.04.2020, p. 2081-2100.

Research output: Contribution to journalArticle

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AU - Fei, Weiyin

AU - Hu, Liangjian

AU - Mao, Xuerong

AU - Xia, Dengfeng

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KW - Brownian motion

KW - stochastic differential delay equation

KW - truncated Euler-Maruyama

KW - Khasminskii-type condition

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Fei W, Hu L, Mao X, Xia D. Advances in the truncated Euler-Maruyama method for stochastic differential delay equations. Communications on Pure and Applied Analysis. 2020 Apr 30;19(4):2081-2100. https://doi.org/10.3934/cpaa.2020092