The truncated Euler-Maruyama method for stochastic differential delay equations

Qian Guo, Xuerong Mao, Rongxian Yue

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Abstract

The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao [15], 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 Lp) of the numerical solutions for the SDDEs under this generalized condition. In this paper, we will use the truncated EM method developed by Mao [16] to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition.
Original languageEnglish
Number of pages26
JournalNumerical Algorithms
Early online date11 Aug 2017
DOIs
Publication statusE-pub ahead of print - 11 Aug 2017

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Keywords

  • Brownian motion
  • stochastic differential delay equation
  • Itô's formula
  • truncated Euler-Maruyama
  • Khasminskii-type condition

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