On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients

Hoang Long Ngo; Dai Taguchi

doi:10.1016/j.matcom.2019.01.012

On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients

Hoang Long Ngo, Dai Taguchi

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

1 Citation (Scopus)

Abstract

We consider the strong rate of convergence of the Euler–Maruyama approximation for stochastic differential equations with possibly discontinuous drift and Hölder continuous diffusion coefficient. In particular, we show that the rates obtained in some recent papers can be improved under an additional assumption that the diffusion coefficient is of bounded variation.

Original language	English
Pages (from-to)	102-112
Number of pages	11
Journal	Mathematics and Computers in Simulation
Volume	161
DOIs	https://doi.org/10.1016/j.matcom.2019.01.012
Publication status	Published - Jul 2019
Externally published	Yes

Keywords

Discontinuous drift coefficient
Euler–Maruyama approximation
Hölder continuous diffusion coefficient
Rate of convergence

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)
Numerical Analysis
Modelling and Simulation
Applied Mathematics

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title = "On the Euler–Maruyama scheme for SDEs with bounded variation and H{\"o}lder continuous coefficients",

abstract = "We consider the strong rate of convergence of the Euler–Maruyama approximation for stochastic differential equations with possibly discontinuous drift and H{\"o}lder continuous diffusion coefficient. In particular, we show that the rates obtained in some recent papers can be improved under an additional assumption that the diffusion coefficient is of bounded variation.",

keywords = "Discontinuous drift coefficient, Euler–Maruyama approximation, H{\"o}lder continuous diffusion coefficient, Rate of convergence",

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

note = "Funding Information: This work was supported by JSPS KAKENHI under Grant Numbers 16J00894 and 17H06833 and by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2017.316 . ",

year = "2019",

month = jul,

doi = "10.1016/j.matcom.2019.01.012",

language = "English",

volume = "161",

pages = "102--112",

journal = "Mathematics and Computers in Simulation",

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T1 - On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients

AU - Ngo, Hoang Long

AU - Taguchi, Dai

N1 - Funding Information: This work was supported by JSPS KAKENHI under Grant Numbers 16J00894 and 17H06833 and by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2017.316 .

PY - 2019/7

Y1 - 2019/7

N2 - We consider the strong rate of convergence of the Euler–Maruyama approximation for stochastic differential equations with possibly discontinuous drift and Hölder continuous diffusion coefficient. In particular, we show that the rates obtained in some recent papers can be improved under an additional assumption that the diffusion coefficient is of bounded variation.

AB - We consider the strong rate of convergence of the Euler–Maruyama approximation for stochastic differential equations with possibly discontinuous drift and Hölder continuous diffusion coefficient. In particular, we show that the rates obtained in some recent papers can be improved under an additional assumption that the diffusion coefficient is of bounded variation.

KW - Discontinuous drift coefficient

KW - Euler–Maruyama approximation

KW - Hölder continuous diffusion coefficient

KW - Rate of convergence

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DO - 10.1016/j.matcom.2019.01.012

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EP - 112

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

ER -

On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients

Abstract

Keywords

ASJC Scopus subject areas

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