Exponential stability of Euler–Maruyama solutions for impulsive stochastic differential equations with delay

This paper establishes a method to study the exponential stability of Euler–Maruyama (EM) method for impulsive stochastic differential equations with delay. By using the properties of M-matrix and stochastic analysis technique, some conditions under which the EM solution is exponentially mean-square...

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Bibliographic Details
Published in:Applied mathematics and computation 2010, Vol.215 (9), p.3425-3432
Main Authors: Zhao, Guihua, Song, M.H., Liu, M.Z.
Format: Article
Language:English
Subjects:
Algebra
Delay
Euler–Maruyama method
Exact sciences and technology
Exponentially mean-square stable
Impulsive stochastic differential equations
Linear and multilinear algebra, matrix theory
M-matrix
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Ordinary differential equations
Sciences and techniques of general use
Sequences, series, summability
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Summary:This paper establishes a method to study the exponential stability of Euler–Maruyama (EM) method for impulsive stochastic differential equations with delay. By using the properties of M-matrix and stochastic analysis technique, some conditions under which the EM solution is exponentially mean-square stable are obtained. Some examples are provided to illustrate the results.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2009.10.037