Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments

Hongling Shi; Minghui Song; Mingzhu Liu

doi:10.1007/s40314-024-02972-4

Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments

Hongling Shi
, Minghui Song^*
, Mingzhu Liu

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

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

Abstract

Adapted the truncation techniques from Mao (2015) and Li et al. (2019), we propose an explicit numerical method, i.e. the truncated Euler–Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs). We establish the strong convergence theory and demonstrate that the convergence rate is 1/2. The mean square exponential stability is investigated. Finally, two numerical experiments are addressed to support the theoretical results.

Original language	English
Article number	23
Journal	Computational and Applied Mathematics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1007/s40314-024-02972-4
State	Published - Feb 2025
Externally published	Yes

Keywords

65C30
65H35
Convergence rate
Local Lipschitz condition
Mean square exponential stability
Strong convergence
Truncated EM method

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10.1007/s40314-024-02972-4

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title = "Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments",

abstract = "Adapted the truncation techniques from Mao (2015) and Li et al. (2019), we propose an explicit numerical method, i.e. the truncated Euler–Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs). We establish the strong convergence theory and demonstrate that the convergence rate is 1/2. The mean square exponential stability is investigated. Finally, two numerical experiments are addressed to support the theoretical results.",

keywords = "65C30, 65H35, Convergence rate, Local Lipschitz condition, Mean square exponential stability, Strong convergence, Truncated EM method",

author = "Hongling Shi and Minghui Song and Mingzhu Liu",

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doi = "10.1007/s40314-024-02972-4",

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T1 - Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments

AU - Shi, Hongling

AU - Song, Minghui

AU - Liu, Mingzhu

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024.

PY - 2025/2

Y1 - 2025/2

N2 - Adapted the truncation techniques from Mao (2015) and Li et al. (2019), we propose an explicit numerical method, i.e. the truncated Euler–Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs). We establish the strong convergence theory and demonstrate that the convergence rate is 1/2. The mean square exponential stability is investigated. Finally, two numerical experiments are addressed to support the theoretical results.

AB - Adapted the truncation techniques from Mao (2015) and Li et al. (2019), we propose an explicit numerical method, i.e. the truncated Euler–Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs). We establish the strong convergence theory and demonstrate that the convergence rate is 1/2. The mean square exponential stability is investigated. Finally, two numerical experiments are addressed to support the theoretical results.

KW - 65C30

KW - 65H35

KW - Convergence rate

KW - Local Lipschitz condition

KW - Mean square exponential stability

KW - Strong convergence

KW - Truncated EM method

UR - https://www.scopus.com/pages/publications/85209119475

U2 - 10.1007/s40314-024-02972-4

DO - 10.1007/s40314-024-02972-4

M3 - 文章

AN - SCOPUS:85209119475

SN - 2238-3603

VL - 44

JO - Computational and Applied Mathematics

JF - Computational and Applied Mathematics

IS - 1

M1 - 23

ER -

Convergence and stability of an explicit numerical method for stochastic differential equations with piecewise continuous arguments

Abstract

Keywords

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