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Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations

Huabin Chen Orcid Logo, Chenggui Yuan Orcid Logo

SIAM Journal on Control and Optimization, Volume: 62, Issue: 2, Pages: 924 - 952

Swansea University Author: Chenggui Yuan Orcid Logo

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DOI (Published version): 10.1137/22m1523066

Abstract

IIn this paper, we provide some sufficient conditions for the existence and uniqueness, the stochastic stability for the global solution of nonlinear neutral stochastic functional differential equation. When the drift term and the diffusion term satisfy a locally Lipschitz condition, and the Lyapuno...

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Published in: SIAM Journal on Control and Optimization
ISSN: 0363-0129 1095-7138
Published: Society for Industrial & Applied Mathematics (SIAM) 2024
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa65806
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Abstract: IIn this paper, we provide some sufficient conditions for the existence and uniqueness, the stochastic stability for the global solution of nonlinear neutral stochastic functional differential equation. When the drift term and the diffusion term satisfy a locally Lipschitz condition, and the Lyapunov monotonicity condition has a sign-changed time-varying coefficient, the existence and uniqueness of the global solution for such equation will be studied by using the Lyapunov-Krasovskii function and the theory of stochastic analysis. The stability in $p$th($p\geq 2$)-moment, the asymptotical stability in $p$th($p\geq 2$)-moment, and the exponential stability in $p$th($p\geq 2$)-moment will be investigated. Three different characterizations for these three kinds of stochastic stability in moment will be established, which are presented in terms of integration conditions, respectively. These results have seldom been reported in the existing literature. In addition, the almost surely exponential stability for the global solution of such equation is also discussed. Some discussions and comparisons are provided. Two examples are given to illustrate the effectiveness of the theoretical results obtained.
Keywords: Nonlinear neutral stochastic functional differential equation; time-varying equation; global solution; existence and uniqueness; stochastic stability
College: Faculty of Science and Engineering
Funders: The first author was partially supported by the National Natural Science Foundation of China (62163027) and the Jiangxi Provincial Natural Science Foundation (20232ACB202006).
Issue: 2
Start Page: 924
End Page: 952