Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients

Hoang Long Ngo; Dai Taguchi

doi:10.1090/mcom3042

Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients

Hoang Long Ngo, Dai Taguchi

Research output: Contribution to journal › Article › peer-review

49 Citations (Scopus)

Abstract

We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is Hölder continuous and uniformly elliptic.

Original language	English
Pages (from-to)	1793-1819
Number of pages	27
Journal	Mathematics of Computation
Volume	85
Issue number	300
DOIs	https://doi.org/10.1090/mcom3042
Publication status	Published - 2016
Externally published	Yes

Keywords

Euler-Maruyama approximation
Irregular coefficient
Rate of convergence
Stochastic differential equation
Strong approximation

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/mcom3042

Cite this

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title = "Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients",

abstract = "We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is H{\"o}lder continuous and uniformly elliptic.",

keywords = "Euler-Maruyama approximation, Irregular coefficient, Rate of convergence, Stochastic differential equation, Strong approximation",

author = "Ngo, {Hoang Long} and Dai Taguchi",

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year = "2016",

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AU - Ngo, Hoang Long

AU - Taguchi, Dai

PY - 2016

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AB - We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is Hölder continuous and uniformly elliptic.

KW - Euler-Maruyama approximation

KW - Irregular coefficient

KW - Rate of convergence

KW - Stochastic differential equation

KW - Strong approximation

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Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients

Abstract

Keywords

ASJC Scopus subject areas

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