Strong convergence of the truncated Euler–Maruyama method for stochastic functional differential equations

Wei Zhang; M. H. Song; M. Z. Liu

doi:10.1080/00207160.2017.1395871

Strong convergence of the truncated Euler–Maruyama method for stochastic functional differential equations

Wei Zhang
, M. H. Song^*
, M. Z. Liu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Heilongjiang University

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

11 Scopus citations

Abstract

In this paper, we establish the truncated Euler–Maruyama (EM) method for stochastic functional differential equation (SFDE) d_y(t) = f (y_t) dt + g(y_t) dB(t) and consider the strong convergence theory for the numerical solutions of SFDEs under the local Lipschitz condition plus Khasminskii-type condition instead of the linear growth condition. The type of convergence specifically addressed in this paper is strong- -L^q> convergence for 2 ≤ q < p, and p is a parameter in Khasminskii-type condition. We also discussed the rates of L_q-convergence for the truncated EM method.

Original language	English
Pages (from-to)	2363-2387
Number of pages	25
Journal	International Journal of Computer Mathematics
Volume	95
Issue number	12
DOIs	https://doi.org/10.1080/00207160.2017.1395871
State	Published - 2 Dec 2018

Keywords

Khasminskii-type condition
Local Lipschitz condition
Stochastic functional differential equation
strong convergence
truncated Euler–Maruyama method

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10.1080/00207160.2017.1395871

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title = "Strong convergence of the truncated Euler–Maruyama method for stochastic functional differential equations",

abstract = "In this paper, we establish the truncated Euler–Maruyama (EM) method for stochastic functional differential equation (SFDE) dy(t) = f (yt) dt + g(yt) dB(t) and consider the strong convergence theory for the numerical solutions of SFDEs under the local Lipschitz condition plus Khasminskii-type condition instead of the linear growth condition. The type of convergence specifically addressed in this paper is strong- -Lq> convergence for 2 ≤ q < p, and p is a parameter in Khasminskii-type condition. We also discussed the rates of Lq-convergence for the truncated EM method.",

keywords = "Khasminskii-type condition, Local Lipschitz condition, Stochastic functional differential equation, strong convergence, truncated Euler–Maruyama method",

author = "Wei Zhang and Song, \{M. H.\} and Liu, \{M. Z.\}",

note = "Publisher Copyright: {\textcopyright} 2017, {\textcopyright} 2017 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2018",

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doi = "10.1080/00207160.2017.1395871",

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T1 - Strong convergence of the truncated Euler–Maruyama method for stochastic functional differential equations

AU - Zhang, Wei

AU - Song, M. H.

AU - Liu, M. Z.

PY - 2018/12/2

Y1 - 2018/12/2

N2 - In this paper, we establish the truncated Euler–Maruyama (EM) method for stochastic functional differential equation (SFDE) dy(t) = f (yt) dt + g(yt) dB(t) and consider the strong convergence theory for the numerical solutions of SFDEs under the local Lipschitz condition plus Khasminskii-type condition instead of the linear growth condition. The type of convergence specifically addressed in this paper is strong- -Lq> convergence for 2 ≤ q < p, and p is a parameter in Khasminskii-type condition. We also discussed the rates of Lq-convergence for the truncated EM method.

AB - In this paper, we establish the truncated Euler–Maruyama (EM) method for stochastic functional differential equation (SFDE) dy(t) = f (yt) dt + g(yt) dB(t) and consider the strong convergence theory for the numerical solutions of SFDEs under the local Lipschitz condition plus Khasminskii-type condition instead of the linear growth condition. The type of convergence specifically addressed in this paper is strong- -Lq> convergence for 2 ≤ q < p, and p is a parameter in Khasminskii-type condition. We also discussed the rates of Lq-convergence for the truncated EM method.

KW - Khasminskii-type condition

KW - Local Lipschitz condition

KW - Stochastic functional differential equation

KW - strong convergence

KW - truncated Euler–Maruyama method

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DO - 10.1080/00207160.2017.1395871

M3 - 文章

AN - SCOPUS:85033663516

SN - 0020-7160

VL - 95

SP - 2363

EP - 2387

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 12

ER -

Strong convergence of the truncated Euler–Maruyama method for stochastic functional differential equations

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Keywords

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