Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion
Abstract G-Brownian motion has potential applications in uncertainty problems and risk measures, which has attracted the attention of many scholars. This study investigates the almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion. Due to the non-...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-10-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-022-01655-5 |
| _version_ | 1811195017030533120 |
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| author | Chao Wei |
| author_facet | Chao Wei |
| author_sort | Chao Wei |
| collection | DOAJ |
| description | Abstract G-Brownian motion has potential applications in uncertainty problems and risk measures, which has attracted the attention of many scholars. This study investigates the almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion. Due to the non-linearity of G-expectation and distribution uncertainty of G-Brownian motion, it is difficult to study this issue. Firstly, the existence of the global unique solution is derived under the linear growth condition and local Lipschitz condition. Secondly, the almost sure exponential stability of the system is analyzed by applying the G-Lyapunov function and G-Itô formula. Finally, an example is introduced to illustrate the stability. The conclusions of this paper can be applied to the stability and risk management of uncertain financial markets. |
| first_indexed | 2024-04-12T00:36:53Z |
| format | Article |
| id | doaj.art-d8b92c98f9174ef1ac85d128c46c4498 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-12T00:36:53Z |
| publishDate | 2022-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-d8b92c98f9174ef1ac85d128c46c44982022-12-22T03:55:08ZengSpringerOpenBoundary Value Problems1687-27702022-10-012022111210.1186/s13661-022-01655-5Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motionChao Wei0School of Mathematics and Statistics, Anyang Normal UniversityAbstract G-Brownian motion has potential applications in uncertainty problems and risk measures, which has attracted the attention of many scholars. This study investigates the almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion. Due to the non-linearity of G-expectation and distribution uncertainty of G-Brownian motion, it is difficult to study this issue. Firstly, the existence of the global unique solution is derived under the linear growth condition and local Lipschitz condition. Secondly, the almost sure exponential stability of the system is analyzed by applying the G-Lyapunov function and G-Itô formula. Finally, an example is introduced to illustrate the stability. The conclusions of this paper can be applied to the stability and risk management of uncertain financial markets.https://doi.org/10.1186/s13661-022-01655-5Nonlinear stochastic systemAlmost sure exponential stabilityG-Brownian motionMarkovian switching |
| spellingShingle | Chao Wei Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion Boundary Value Problems Nonlinear stochastic system Almost sure exponential stability G-Brownian motion Markovian switching |
| title | Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion |
| title_full | Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion |
| title_fullStr | Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion |
| title_full_unstemmed | Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion |
| title_short | Almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by G-Brownian motion |
| title_sort | almost sure exponential stability of nonlinear stochastic delay hybrid systems driven by g brownian motion |
| topic | Nonlinear stochastic system Almost sure exponential stability G-Brownian motion Markovian switching |
| url | https://doi.org/10.1186/s13661-022-01655-5 |
| work_keys_str_mv | AT chaowei almostsureexponentialstabilityofnonlinearstochasticdelayhybridsystemsdrivenbygbrownianmotion |