A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations

X. Mao, C. Yuan

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence. In this note, we will show the rate of convergence still under the local Lipschitz condition, but the local Lipschitz constants of the drift coefficient, valid on balls of radius R, are supposed not to grow faster than log R while those of the diffusion coefficient are not than.
LanguageEnglish
Pages325-333
Number of pages8
JournalStochastic Analysis and Applications
Volume26
Issue number2
DOIs
Publication statusPublished - 2008

Fingerprint

Euler-Maruyama Method
Stochastic Equations
Rate of Convergence
Differential equations
Lipschitz condition
Differential equation
Order of Convergence
Strong Convergence
Diffusion Coefficient
Lipschitz
Euler
Ball
Exact Solution
Radius
Valid
Coefficient
Rate of convergence
Stochastic differential equations
Coefficients

Keywords

  • brownian motion
  • euler-maruyama method
  • lipschitz condition
  • differential equations

Cite this

@article{971d7d56109a45ffb8c6ac9c788b2491,
title = "A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations",
abstract = "The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence. In this note, we will show the rate of convergence still under the local Lipschitz condition, but the local Lipschitz constants of the drift coefficient, valid on balls of radius R, are supposed not to grow faster than log R while those of the diffusion coefficient are not than.",
keywords = "brownian motion, euler-maruyama method, lipschitz condition, differential equations",
author = "X. Mao and C. Yuan",
year = "2008",
doi = "10.1080/07362990701857251",
language = "English",
volume = "26",
pages = "325--333",
journal = "Stochastic Analysis and Applications",
issn = "0736-2994",
number = "2",

}

A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations. / Mao, X.; Yuan, C.

In: Stochastic Analysis and Applications, Vol. 26, No. 2, 2008, p. 325-333.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations

AU - Mao, X.

AU - Yuan, C.

PY - 2008

Y1 - 2008

N2 - The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence. In this note, we will show the rate of convergence still under the local Lipschitz condition, but the local Lipschitz constants of the drift coefficient, valid on balls of radius R, are supposed not to grow faster than log R while those of the diffusion coefficient are not than.

AB - The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence. In this note, we will show the rate of convergence still under the local Lipschitz condition, but the local Lipschitz constants of the drift coefficient, valid on balls of radius R, are supposed not to grow faster than log R while those of the diffusion coefficient are not than.

KW - brownian motion

KW - euler-maruyama method

KW - lipschitz condition

KW - differential equations

UR - http://dx.doi.org/10.1080/07362990701857251

U2 - 10.1080/07362990701857251

DO - 10.1080/07362990701857251

M3 - Article

VL - 26

SP - 325

EP - 333

JO - Stochastic Analysis and Applications

T2 - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

SN - 0736-2994

IS - 2

ER -