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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
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URI: https://cronfa.swan.ac.uk/Record/cronfa65806
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spelling v2 65806 2024-03-11 Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations 22b571d1cba717a58e526805bd9abea0 0000-0003-0486-5450 Chenggui Yuan Chenggui Yuan true false 2024-03-11 SMA 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. Journal Article SIAM Journal on Control and Optimization 62 2 924 952 Society for Industrial & Applied Mathematics (SIAM) 0363-0129 1095-7138 Nonlinear neutral stochastic functional differential equation; time-varying equation; global solution; existence and uniqueness; stochastic stability 30 4 2024 2024-04-30 10.1137/22m1523066 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University The first author was partially supported by the National Natural Science Foundation of China (62163027) and the Jiangxi Provincial Natural Science Foundation (20232ACB202006). 2024-04-24T15:24:58.8966002 2024-03-11T08:40:15.9534542 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Huabin Chen 0000-0002-8785-4126 1 Chenggui Yuan 0000-0003-0486-5450 2 65806__29674__8a9df31712de4777bea141810c591c39.pdf Stability-RIS-24.pdf 2024-03-11T08:58:38.5382727 Output 184227 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/
title Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
spellingShingle Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
Chenggui Yuan
title_short Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
title_full Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
title_fullStr Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
title_full_unstemmed Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
title_sort Stability Analysis for Nonlinear Neutral Stochastic Functional Differential Equations
author_id_str_mv 22b571d1cba717a58e526805bd9abea0
author_id_fullname_str_mv 22b571d1cba717a58e526805bd9abea0_***_Chenggui Yuan
author Chenggui Yuan
author2 Huabin Chen
Chenggui Yuan
format Journal article
container_title SIAM Journal on Control and Optimization
container_volume 62
container_issue 2
container_start_page 924
publishDate 2024
institution Swansea University
issn 0363-0129
1095-7138
doi_str_mv 10.1137/22m1523066
publisher Society for Industrial & Applied Mathematics (SIAM)
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2024-04-30T15:24:58Z
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score 11.037056

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