The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients

Hao Yang; Fuke Wu; Peter E. Kloeden; Xuerong Mao

doi:10.1016/j.cam.2019.112379

The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients

Hao Yang, Fuke Wu, Peter E. Kloeden, Xuerong Mao

Mathematics And Statistics

Research output: Contribution to journal › Article

Abstract

In stochastic financial and biological models, the diffusion coefficients often involve the term √x, or more general |x|^r for r ∈ (0,1), which is non-Lipschitz. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) approximation first proposed by Mao (2015) for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the Hölder continuous diffusion coefficients.

Original language	English
Article number	112379
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	366
Early online date	16 Aug 2019
DOIs	https://doi.org/10.1016/j.cam.2019.112379
Publication status	Published - 1 Mar 2020

Keywords

strong convergence
truncated EM
Hölder diffusion coefficients

Access to Document

10.1016/j.cam.2019.112379

Embargoed Document

Yang-etal-JCAM-2019-The-truncated-Euler-Maruyama-method-for-stochastic-differential-equations
Accepted author manuscript, 300 KB
Licence: CC BY-NC-ND 4.0
Embargo ends: 16/08/20

Fingerprint Dive into the research topics of 'The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients'. Together they form a unique fingerprint.

Cite this

Yang, H., Wu, F., Kloeden, P. E., & Mao, X. (2020). The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients. Journal of Computational and Applied Mathematics, 366, [112379]. https://doi.org/10.1016/j.cam.2019.112379

@article{fa40c0a7d4fa4a1b9fb218e93eb9c5a1,

title = "The truncated Euler-Maruyama method for stochastic differential equations with H{\"o}lder diffusion coefficients",

abstract = "In stochastic financial and biological models, the diffusion coefficients often involve the term √x, or more general |x|r for r ∈ (0,1), which is non-Lipschitz. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) approximation first proposed by Mao (2015) for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the H{\"o}lder continuous diffusion coefficients. ",

keywords = "strong convergence, truncated EM, H{\"o}lder diffusion coefficients",

author = "Hao Yang and Fuke Wu and Kloeden, {Peter E.} and Xuerong Mao",

year = "2020",

month = "3",

day = "1",

doi = "10.1016/j.cam.2019.112379",

language = "English",

volume = "366",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

}

TY - JOUR

T1 - The truncated Euler-Maruyama method for stochastic differential equations with Hölder diffusion coefficients

AU - Yang, Hao

AU - Wu, Fuke

AU - Kloeden, Peter E.

AU - Mao, Xuerong

PY - 2020/3/1

Y1 - 2020/3/1

N2 - In stochastic financial and biological models, the diffusion coefficients often involve the term √x, or more general |x|r for r ∈ (0,1), which is non-Lipschitz. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) approximation first proposed by Mao (2015) for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the Hölder continuous diffusion coefficients.

AB - In stochastic financial and biological models, the diffusion coefficients often involve the term √x, or more general |x|r for r ∈ (0,1), which is non-Lipschitz. In this paper, we study the strong convergence of the truncated Euler–Maruyama (EM) approximation first proposed by Mao (2015) for one-dimensional stochastic differential equations (SDEs) with superlinearly growing drifts and the Hölder continuous diffusion coefficients.

KW - strong convergence

KW - truncated EM

KW - Hölder diffusion coefficients

U2 - 10.1016/j.cam.2019.112379

DO - 10.1016/j.cam.2019.112379

M3 - Article

VL - 366

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 112379

ER -