On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations

In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness theorem as well as the almost surely asymptotic behavior for the global solution of highly nonlinear stochastic differential equations with time-varying delay and Markovian swi...

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Autores: Zhang, Tian, Chen, Huabin, Yuan, Chenggui, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/92690
Acceso en línea:https://hdl.handle.net/11441/92690
https://doi.org/10.3934/dcdsb.2019062
Access Level:acceso abierto
Palabra clave:Stochastic differential equations
Time-varying delay
Asymptotic behavior
Stability
Markov switching
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spelling On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equationsZhang, TianChen, HuabinYuan, ChengguiCaraballo Garrido, TomásStochastic differential equationsTime-varying delayAsymptotic behaviorStabilityMarkov switchingIn this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness theorem as well as the almost surely asymptotic behavior for the global solution of highly nonlinear stochastic differential equations with time-varying delay and Markovian switching are discussed by using the Lyapunov function and some stochastic analysis techniques. Two integral lemmas are firstly established to overcome the difficulty stemming from the coexistence of the stochastic perturbation and the time-varying delay. Then, without any redundant restrictive condition on the time-varying delay, by utilizing the integral inequality, the exponential stability in pth(p ≥ 1)-moment for such equations is investigated. By employing the nonnegative semi-martingale convergence theorem, the almost sure exponential stability is analyzed. Finally, two examples are given to show the usefulness of the results obtained.National Natural Science Foundation of ChinaNatural Science Foundation of Jiangxi Province of ChinaFoundation of Jiangxi Provincial Educations of ChinaMinisterio de Economía y Competitividad (MINECO). EspañaJunta de AndalucíaAmerican Institute of Mathematical SciencesEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/92690https://doi.org/10.3934/dcdsb.2019062reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems - Series B, 24 (10), 5355-5375.61364005114012926177340120171BAB20100720171BCB23001GJJ160061GJJ14155MTM2015-63723-PP12-FQM-1492https://www.aimsciences.org/article/doi/10.3934/dcdsb.2019062info:eu-repo/semantics/openAccessoai:idus.us.es:11441/926902026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
title On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
spellingShingle On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
Zhang, Tian
Stochastic differential equations
Time-varying delay
Asymptotic behavior
Stability
Markov switching
title_short On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
title_full On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
title_fullStr On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
title_full_unstemmed On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
title_sort On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
dc.creator.none.fl_str_mv Zhang, Tian
Chen, Huabin
Yuan, Chenggui
Caraballo Garrido, Tomás
author Zhang, Tian
author_facet Zhang, Tian
Chen, Huabin
Yuan, Chenggui
Caraballo Garrido, Tomás
author_role author
author2 Chen, Huabin
Yuan, Chenggui
Caraballo Garrido, Tomás
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Stochastic differential equations
Time-varying delay
Asymptotic behavior
Stability
Markov switching
topic Stochastic differential equations
Time-varying delay
Asymptotic behavior
Stability
Markov switching
description In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness theorem as well as the almost surely asymptotic behavior for the global solution of highly nonlinear stochastic differential equations with time-varying delay and Markovian switching are discussed by using the Lyapunov function and some stochastic analysis techniques. Two integral lemmas are firstly established to overcome the difficulty stemming from the coexistence of the stochastic perturbation and the time-varying delay. Then, without any redundant restrictive condition on the time-varying delay, by utilizing the integral inequality, the exponential stability in pth(p ≥ 1)-moment for such equations is investigated. By employing the nonnegative semi-martingale convergence theorem, the almost sure exponential stability is analyzed. Finally, two examples are given to show the usefulness of the results obtained.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/92690
https://doi.org/10.3934/dcdsb.2019062
url https://hdl.handle.net/11441/92690
https://doi.org/10.3934/dcdsb.2019062
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems - Series B, 24 (10), 5355-5375.
61364005
11401292
61773401
20171BAB201007
20171BCB23001
GJJ160061
GJJ14155
MTM2015-63723-P
P12-FQM-1492
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2019062
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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