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

2 Citations (Scopus)

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 statusPublished - 30 Apr 2020

Keywords

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

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