Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay

Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a f...
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Autor*in:	Mahmoud, Ayman M. [verfasserIn] Adewumi, Adebayo O. Ademola, Adeleke T.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Stochastic asymptotic stability Stochastic differential equation Constant delay Lyapunov functional

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Journal of inequalities and applications - Heidelberg : Springer, 2005, 2023(2023), 1 vom: 15. Nov.
Übergeordnetes Werk:	volume:2023 ; year:2023 ; number:1 ; day:15 ; month:11

Links:	Volltext

DOI / URN:	10.1186/s13660-023-03061-6

Katalog-ID:	SPR053755189

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520			\|a Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result.
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allfields	10.1186/s13660-023-03061-6 doi (DE-627)SPR053755189 (SPR)s13660-023-03061-6-e DE-627 ger DE-627 rakwb eng Mahmoud, Ayman M. verfasserin aut Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. Stochastic asymptotic stability (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Constant delay (dpeaa)DE-He213 Lyapunov functional (dpeaa)DE-He213 Adewumi, Adebayo O. aut Ademola, Adeleke T. aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 15. Nov. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:15 month:11 https://dx.doi.org/10.1186/s13660-023-03061-6 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 15 11
spelling	10.1186/s13660-023-03061-6 doi (DE-627)SPR053755189 (SPR)s13660-023-03061-6-e DE-627 ger DE-627 rakwb eng Mahmoud, Ayman M. verfasserin aut Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. Stochastic asymptotic stability (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Constant delay (dpeaa)DE-He213 Lyapunov functional (dpeaa)DE-He213 Adewumi, Adebayo O. aut Ademola, Adeleke T. aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 15. Nov. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:15 month:11 https://dx.doi.org/10.1186/s13660-023-03061-6 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 15 11
allfields_unstemmed	10.1186/s13660-023-03061-6 doi (DE-627)SPR053755189 (SPR)s13660-023-03061-6-e DE-627 ger DE-627 rakwb eng Mahmoud, Ayman M. verfasserin aut Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. Stochastic asymptotic stability (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Constant delay (dpeaa)DE-He213 Lyapunov functional (dpeaa)DE-He213 Adewumi, Adebayo O. aut Ademola, Adeleke T. aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 15. Nov. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:15 month:11 https://dx.doi.org/10.1186/s13660-023-03061-6 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 15 11
allfieldsGer	10.1186/s13660-023-03061-6 doi (DE-627)SPR053755189 (SPR)s13660-023-03061-6-e DE-627 ger DE-627 rakwb eng Mahmoud, Ayman M. verfasserin aut Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. Stochastic asymptotic stability (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Constant delay (dpeaa)DE-He213 Lyapunov functional (dpeaa)DE-He213 Adewumi, Adebayo O. aut Ademola, Adeleke T. aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 15. Nov. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:15 month:11 https://dx.doi.org/10.1186/s13660-023-03061-6 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 15 11
allfieldsSound	10.1186/s13660-023-03061-6 doi (DE-627)SPR053755189 (SPR)s13660-023-03061-6-e DE-627 ger DE-627 rakwb eng Mahmoud, Ayman M. verfasserin aut Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. Stochastic asymptotic stability (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Constant delay (dpeaa)DE-He213 Lyapunov functional (dpeaa)DE-He213 Adewumi, Adebayo O. aut Ademola, Adeleke T. aut Enthalten in Journal of inequalities and applications Heidelberg : Springer, 2005 2023(2023), 1 vom: 15. Nov. (DE-627)320977056 (DE-600)2028512-7 1029-242X nnns volume:2023 year:2023 number:1 day:15 month:11 https://dx.doi.org/10.1186/s13660-023-03061-6 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2111 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2023 2023 1 15 11
language	English
source	Enthalten in Journal of inequalities and applications 2023(2023), 1 vom: 15. Nov. volume:2023 year:2023 number:1 day:15 month:11
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author	Mahmoud, Ayman M.
spellingShingle	Mahmoud, Ayman M. misc Stochastic asymptotic stability misc Stochastic differential equation misc Constant delay misc Lyapunov functional Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay
authorStr	Mahmoud, Ayman M.
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topic_title	Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay Stochastic asymptotic stability (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Constant delay (dpeaa)DE-He213 Lyapunov functional (dpeaa)DE-He213
topic	misc Stochastic asymptotic stability misc Stochastic differential equation misc Constant delay misc Lyapunov functional
topic_unstemmed	misc Stochastic asymptotic stability misc Stochastic differential equation misc Constant delay misc Lyapunov functional
topic_browse	misc Stochastic asymptotic stability misc Stochastic differential equation misc Constant delay misc Lyapunov functional
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title	Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay
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title_full	Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay
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author_browse	Mahmoud, Ayman M. Adewumi, Adebayo O. Ademola, Adeleke T.
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author-letter	Mahmoud, Ayman M.
doi_str_mv	10.1186/s13660-023-03061-6
title_sort	stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay
title_auth	Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay
abstract	Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. © The Author(s) 2023
abstractGer	Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. © The Author(s) 2023
abstract_unstemmed	Abstract In this paper, we present sufficient conditions to ensure the stochastic asymptotic stability of the zero solution for a specific type of fourth-order stochastic differential equation (SDE) with constant delay. By reducing the fourth-order SDE to a system of first-order SDEs, we utilize a fourth-order quadratic function to derive an appropriate Lyapunov functional. This functional is then employed to establish standard criteria for the nonlinear functions present in the SDE. The stability result obtained in this study is novel and extends the existing findings on stability in fourth-order differential equations. Additionally, we provide an illustrative example to demonstrate the significance and accuracy of our main result. © The Author(s) 2023
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title_short	Stochastic stability of solutions for a fourth-order stochastic differential equation with constant delay
url	https://dx.doi.org/10.1186/s13660-023-03061-6
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author2	Adewumi, Adebayo O. Ademola, Adeleke T.
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