Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise
In this paper, stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) is discussed. In contrast to the white noise examined in previous literature, we incorporate colored noise into the highly nonlinear hybrid NSDDEs. Under some assumptions, we can show that hi...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025291 |
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| author | Siru Li Tian Xu Ailong Wu |
| author_facet | Siru Li Tian Xu Ailong Wu |
| author_sort | Siru Li |
| collection | DOAJ |
| description | In this paper, stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) is discussed. In contrast to the white noise examined in previous literature, we incorporate colored noise into the highly nonlinear hybrid NSDDEs. Under some assumptions, we can show that highly nonlinear hybrid NSDDEs have a unique global solution. Meanwhile, we establish some criteria related to noise-to-state stability (NSS) of global solutions. Additionally, some theorems are given to guarantee asymptotic stability in $ L^{\hat{\alpha}} $ and almost surely asymptotic stability of global solution. These related discriminant rules are delay-dependent. Finally, an example is provided to demonstrate the validity of theoretical results. |
| format | Article |
| id | doaj-art-b4a1d0f41a424d2baded83832ef1467f |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-b4a1d0f41a424d2baded83832ef1467f2025-08-20T03:16:58ZengAIMS PressAIMS Mathematics2473-69882025-03-011036379640510.3934/math.2025291Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noiseSiru Li0Tian Xu1Ailong Wu2School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaSchool of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaSchool of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, ChinaIn this paper, stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) is discussed. In contrast to the white noise examined in previous literature, we incorporate colored noise into the highly nonlinear hybrid NSDDEs. Under some assumptions, we can show that highly nonlinear hybrid NSDDEs have a unique global solution. Meanwhile, we establish some criteria related to noise-to-state stability (NSS) of global solutions. Additionally, some theorems are given to guarantee asymptotic stability in $ L^{\hat{\alpha}} $ and almost surely asymptotic stability of global solution. These related discriminant rules are delay-dependent. Finally, an example is provided to demonstrate the validity of theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2025291noise-to-state stabilityasymptotic stabilityalmost surely stabilityneutral stochastic differential delay equations |
| spellingShingle | Siru Li Tian Xu Ailong Wu Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise AIMS Mathematics noise-to-state stability asymptotic stability almost surely stability neutral stochastic differential delay equations |
| title | Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise |
| title_full | Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise |
| title_fullStr | Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise |
| title_full_unstemmed | Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise |
| title_short | Existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise |
| title_sort | existence and asymptotic properties of global solution for hybrid neutral stochastic differential delay equations with colored noise |
| topic | noise-to-state stability asymptotic stability almost surely stability neutral stochastic differential delay equations |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025291 |
| work_keys_str_mv | AT siruli existenceandasymptoticpropertiesofglobalsolutionforhybridneutralstochasticdifferentialdelayequationswithcolorednoise AT tianxu existenceandasymptoticpropertiesofglobalsolutionforhybridneutralstochasticdifferentialdelayequationswithcolorednoise AT ailongwu existenceandasymptoticpropertiesofglobalsolutionforhybridneutralstochasticdifferentialdelayequationswithcolorednoise |