Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments

被引：7

作者：

Geng, Yidan ^{[1
]}

Song, Minghui ^{[1
]}

Lu, Yulan ^{[2
]}

Liu, Mingzhu ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2021年 / 14卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Stochastic differential equations with piecewise continuous argument; local Lipschitz condition; Khasminskii-type condition; truncated Euler-Maruyama method; convergence and stability; TIME; SDES; STABILIZATION; RATES;

D O I：

10.4208/nmtma.OA-2019-0108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop the truncated Euler-Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The order of convergence is obtained. Moreover, we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs. Numerical examples are provided to support our conclusions.

引用

页码：194 / 218

页数：25

共 28 条

[1] ON TAMED EULER APPROXIMATIONS OF SDES DRIVEN BY LEVY NOISE WITH APPLICATIONS TO DELAY EQUATIONS [J].

Dareiotis, Konstantinos ;

Kumar, Chaman ;

Sabanis, Sotirios .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (03) :1840-1872

[2] Strong Convergence of the Semi-Implicit Euler Method for a Kind of Stochastic Volterra Integro-Differential Equations [J].

Gao, Jianfang ;

Ma, Shufang ;

Liang, Hui .

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2019, 12 (02) :547-565

[3] The partially truncated Euler-Maruyama method and its stability and boundedness [J].

Guo, Qian ;

Liu, Wei ;

Mao, Xuerong ;

Yue, Rongxian .

APPLIED NUMERICAL MATHEMATICS, 2017, 115 :235-251

[4] Strong convergence of Euler-type methods for nonlinear stochastic differential equations [J].

Higham, DJ ;

Mao, XR ;

Stuart, AM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (03) :1041-1063

[5] Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations [J].

Hu, Liangjian ;

Li, Xiaoyue ;

Mao, Xuerong .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 337 :274-289

[6]

Hu YZ, 1996, PROG PROBAB, V38, P183

[7] STRONG CONVERGENCE OF AN EXPLICIT NUMERICAL METHOD FOR SDES WITH NONGLOBALLY LIPSCHITZ CONTINUOUS COEFFICIENTS [J].

Hutzenthaler, Martin ;

Jentzen, Arnulf ;

Kloeden, Peter E. .

ANNALS OF APPLIED PROBABILITY, 2012, 22 (04) :1611-1641

[8] Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients [J].

Hutzenthaler, Martin ;

Jentzen, Arnulf ;

Kloeden, Peter E. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2011, 467 (2130) :1563-1576

[9] On quasi-periodic solutions of differential equations with piecewise constant argument [J].

Küpper, T ;

Yuan, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 267 (01) :173-193

[10] Strong convergence rates of modified truncated EM method for stochastic differential equations [J].

Lan, Guangqiang ;

Xia, Fang .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 334 :1-17

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