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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2019-12-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2019.1652453 |
| _version_ | 1819276902063407104 |
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| author | Osman Tunç Cemil Tunç |
| author_facet | Osman Tunç Cemil Tunç |
| author_sort | Osman Tunç |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T23:47:35Z |
| format | Article |
| id | doaj.art-a13d903cda604621911d89a198377e98 |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-12-23T23:47:35Z |
| publishDate | 2019-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-a13d903cda604621911d89a198377e982022-12-21T17:25:29ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552019-12-0113187588210.1080/16583655.2019.16524531652453On the asymptotic stability of solutions of stochastic differential delay equations of second orderOsman Tunç0Cemil Tunç1Van Yuzuncu Yil UniversityVan Yuzuncu Yil UniversityIn 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.http://dx.doi.org/10.1080/16583655.2019.1652453stochastic delay differential equationsecond orderstochastically stabilitystochastically asymptotically stabilitylyapunov-krasovskii functional |
| spellingShingle | Osman Tunç Cemil Tunç On the asymptotic stability of solutions of stochastic differential delay equations of second order Journal of Taibah University for Science stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional |
| title | On the asymptotic stability of solutions of stochastic differential delay equations of second order |
| title_full | On the asymptotic stability of solutions of stochastic differential delay equations of second order |
| title_fullStr | On the asymptotic stability of solutions of stochastic differential delay equations of second order |
| title_full_unstemmed | On the asymptotic stability of solutions of stochastic differential delay equations of second order |
| title_short | On the asymptotic stability of solutions of stochastic differential delay equations of second order |
| title_sort | on the asymptotic stability of solutions of stochastic differential delay equations of second order |
| topic | stochastic delay differential equation second order stochastically stability stochastically asymptotically stability lyapunov-krasovskii functional |
| url | http://dx.doi.org/10.1080/16583655.2019.1652453 |
| work_keys_str_mv | AT osmantunc ontheasymptoticstabilityofsolutionsofstochasticdifferentialdelayequationsofsecondorder AT cemiltunc ontheasymptoticstabilityofsolutionsofstochasticdifferentialdelayequationsofsecondorder |