The truncated Euler-Maruyama method for stochastic differential delay equations

Qian Guo, Xuerong Mao, Rongxian Yue

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
LanguageEnglish
Number of pages26
JournalNumerical Algorithms
Early online date11 Aug 2017
DOIs
Publication statusE-pub ahead of print - 11 Aug 2017

Fingerprint

Euler-Maruyama Method
Stochastic Differential Delay Equations
Numerical Solution
Strong Convergence
Euler
Converge

Keywords

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

Cite this

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The truncated Euler-Maruyama method for stochastic differential delay equations. / Guo, Qian; Mao, Xuerong; Yue, Rongxian.

In: Numerical Algorithms, 11.08.2017.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The truncated Euler-Maruyama method for stochastic differential delay equations

AU - Guo, Qian

AU - Mao, Xuerong

AU - Yue, Rongxian

PY - 2017/8/11

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N2 - 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.

AB - 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.

KW - Brownian motion

KW - stochastic differential delay equation

KW - Itô's formula

KW - truncated Euler-Maruyama

KW - Khasminskii-type condition

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