A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations

This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation....

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 10; no. 6; p. 866
Main Authors: Wang, Qi, Chen, Huabin, Yuan, Chenggui
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.03.2022
Subjects:
Approximation
Differential equations
discrete Razumikhin-type theorem
Euler–Maruyama method
exponential stability
Food science
neutral stochastic functional differential equations
numerical solution
Random variables
Stability analysis
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation. In addition, the Borel–Cantelli lemma and the stochastic analysis theory are incorporated to discuss the almost sure exponential stability for this numerical solution of such equations.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math10060866