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

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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

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10.1016/j.cam.2019.112379

Yang-etal-JCAM-2019-The-truncated-Euler-Maruyama-method-for-stochastic-differential-equationsAccepted author manuscript, 300 KBLicence: CC BY-NC-ND 4.0

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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. ",

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AU - Yang, Hao

AU - Wu, Fuke

AU - Kloeden, Peter E.

AU - Mao, Xuerong

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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

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KW - Hölder diffusion coefficients

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