On the asymptotic stability of solutions of stochastic differential delay equations of second order

In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based...
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Gespeichert in:

Autor*in:	Osman Tunç [verfasserIn] Cemil Tunç [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional

Übergeordnetes Werk:	In: Journal of Taibah University for Science - Taylor & Francis Group, 2016, 13(2019), 1, Seite 875-882
Übergeordnetes Werk:	volume:13 ; year:2019 ; number:1 ; pages:875-882

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1080/16583655.2019.1652453

Katalog-ID:	DOAJ013590898

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allfields	10.1080/16583655.2019.1652453 doi (DE-627)DOAJ013590898 (DE-599)DOAJa13d903cda604621911d89a198377e98 DE-627 ger DE-627 rakwb eng Q1-390 Osman Tunç verfasserin aut On the asymptotic stability of solutions of stochastic differential delay equations of second order 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature. stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional Science (General) Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 13(2019), 1, Seite 875-882 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:13 year:2019 number:1 pages:875-882 https://doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/article/a13d903cda604621911d89a198377e98 kostenfrei http://dx.doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 13 2019 1 875-882
spelling	10.1080/16583655.2019.1652453 doi (DE-627)DOAJ013590898 (DE-599)DOAJa13d903cda604621911d89a198377e98 DE-627 ger DE-627 rakwb eng Q1-390 Osman Tunç verfasserin aut On the asymptotic stability of solutions of stochastic differential delay equations of second order 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature. stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional Science (General) Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 13(2019), 1, Seite 875-882 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:13 year:2019 number:1 pages:875-882 https://doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/article/a13d903cda604621911d89a198377e98 kostenfrei http://dx.doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 13 2019 1 875-882
allfields_unstemmed	10.1080/16583655.2019.1652453 doi (DE-627)DOAJ013590898 (DE-599)DOAJa13d903cda604621911d89a198377e98 DE-627 ger DE-627 rakwb eng Q1-390 Osman Tunç verfasserin aut On the asymptotic stability of solutions of stochastic differential delay equations of second order 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature. stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional Science (General) Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 13(2019), 1, Seite 875-882 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:13 year:2019 number:1 pages:875-882 https://doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/article/a13d903cda604621911d89a198377e98 kostenfrei http://dx.doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 13 2019 1 875-882
allfieldsGer	10.1080/16583655.2019.1652453 doi (DE-627)DOAJ013590898 (DE-599)DOAJa13d903cda604621911d89a198377e98 DE-627 ger DE-627 rakwb eng Q1-390 Osman Tunç verfasserin aut On the asymptotic stability of solutions of stochastic differential delay equations of second order 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature. stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional Science (General) Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 13(2019), 1, Seite 875-882 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:13 year:2019 number:1 pages:875-882 https://doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/article/a13d903cda604621911d89a198377e98 kostenfrei http://dx.doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 13 2019 1 875-882
allfieldsSound	10.1080/16583655.2019.1652453 doi (DE-627)DOAJ013590898 (DE-599)DOAJa13d903cda604621911d89a198377e98 DE-627 ger DE-627 rakwb eng Q1-390 Osman Tunç verfasserin aut On the asymptotic stability of solutions of stochastic differential delay equations of second order 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature. stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional Science (General) Cemil Tunç verfasserin aut In Journal of Taibah University for Science Taylor & Francis Group, 2016 13(2019), 1, Seite 875-882 (DE-627)835589021 (DE-600)2834710-9 16583655 nnns volume:13 year:2019 number:1 pages:875-882 https://doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/article/a13d903cda604621911d89a198377e98 kostenfrei http://dx.doi.org/10.1080/16583655.2019.1652453 kostenfrei https://doaj.org/toc/1658-3655 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 13 2019 1 875-882
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author	Osman Tunç
spellingShingle	Osman Tunç misc Q1-390 misc stochastic delay differential equation misc second order misc stochastically stability misc stochastically asymptotically stability misc lyapunov-krasovskii functional misc Science (General) On the asymptotic stability of solutions of stochastic differential delay equations of second order
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topic_title	Q1-390 On the asymptotic stability of solutions of stochastic differential delay equations of second order stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional
topic	misc Q1-390 misc stochastic delay differential equation misc second order misc stochastically stability misc stochastically asymptotically stability misc lyapunov-krasovskii functional misc Science (General)
topic_unstemmed	misc Q1-390 misc stochastic delay differential equation misc second order misc stochastically stability misc stochastically asymptotically stability misc lyapunov-krasovskii functional misc Science (General)
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title	On the asymptotic stability of solutions of stochastic differential delay equations of second order
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title_full	On the asymptotic stability of solutions of stochastic differential delay equations of second order
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title_sort	on the asymptotic stability of solutions of stochastic differential delay equations of second order
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title_auth	On the asymptotic stability of solutions of stochastic differential delay equations of second order
abstract	In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature.
abstractGer	In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature.
abstract_unstemmed	In this paper, we consider a non-linear stochastic differential delay equation (SDDE) of second order. We derive new sufficient conditions which guarantee stochastically stability and stochastically asymptotically stability of the zero solution of that SDDE. Here, the technique of the proof is based on the definition of a suitable Lyapunov-Krasovskii functional, which gives meaningful results for the problem under consideration. The derived results extend and improve some result of in the relevant literature, which are related to the qualitative properties of solutions of a SDDE of second order. The results of this paper are new and have novelty, and they do a contribution to the topic and relevant literature. As an application, an example is given to show the effectiveness and applicability of the obtained results. Finally, by the results of this paper, we extend and improve some recent results that can be found in the relevant literature.
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title_short	On the asymptotic stability of solutions of stochastic differential delay equations of second order
url	https://doi.org/10.1080/16583655.2019.1652453 https://doaj.org/article/a13d903cda604621911d89a198377e98 http://dx.doi.org/10.1080/16583655.2019.1652453 https://doaj.org/toc/1658-3655
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On the asymptotic stability of solutions of stochastic differential delay equations of second order

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