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

被引：8

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

[21]

MYSHKIS AD, 1977, RUSS MATH SURV, V32, P181

[22] Time-Stepping Error Bound for a Stochastic Parabolic Volterra Equation Disturbed by Fractional Brownian Motions [J].

Qi, Ruisheng ;

Lin, Qiu .

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2019, 12 (03) :778-796

[23] Stabilization of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay [J].

Qiu, Qinwei ;

Liu, Wei ;

Hu, Liangjian ;

Mao, Xuerong ;

You, Surong .

STATISTICS & PROBABILITY LETTERS, 2016, 115 :16-26

[24] Convergence of the Tamed Euler Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Non-global Lipschitz Continuous Coefficients [J].

Song, M. H. ;

Lu, Y. L. ;

Liu, M. Z. .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (05) :517-536

[25] Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller [J].

Su, Huan ;

Mao, Xuerong ;

Li, Wenxue .

CHAOS, 2016, 26 (11)

[26] A FUNDAMENTAL MEAN-SQUARE CONVERGENCE THEOREM FOR SDEs WITH LOCALLY LIPSCHITZ COEFFICIENTS AND ITS APPLICATIONS [J].

Tretyakov, M. V. ;

Zhang, Z. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (06) :3135-3162

[27]

Wiener J., 1993, GEN SOLUTIONS FUNCTI

[28] STABILIZATION OF HYBRID SYSTEMS BY FEEDBACK CONTROL BASED ON DISCRETE-TIME STATE OBSERVATIONS [J].

You, Surong ;

Liu, Wei ;

Lu, Jianqiu ;

Mao, Xuerong ;

Qiu, Qinwei .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (02) :905-925

← 1 2 3 →