The truncated Euler-Maruyama method for stochastic differential delay equations

Qian Guo; Xuerong Mao; Rongxian Yue

doi:10.1007/s11075-017-0391-0

The truncated Euler-Maruyama method for stochastic differential delay equations

Qian Guo, Xuerong Mao, Rongxian Yue

Mathematics And Statistics

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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 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 [16] to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition.

Original language	English
Number of pages	26
Journal	Numerical Algorithms
Early online date	11 Aug 2017
DOIs	https://doi.org/10.1007/s11075-017-0391-0
Publication status	E-pub ahead of print - 11 Aug 2017

Keywords

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

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title = "The truncated Euler-Maruyama method for stochastic differential delay equations",

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.",

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author = "Qian Guo and Xuerong Mao and Rongxian Yue",

year = "2017",

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doi = "10.1007/s11075-017-0391-0",

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

AU - Guo, Qian

AU - Mao, Xuerong

AU - Yue, Rongxian

PY - 2017/8/11

Y1 - 2017/8/11

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

UR - https://link.springer.com/journal/11075

U2 - 10.1007/s11075-017-0391-0

DO - 10.1007/s11075-017-0391-0

M3 - Article

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

ER -

The truncated Euler-Maruyama method for stochastic differential delay equations

Abstract

Keywords

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