About one unsolved problem in asymptotic p-stability of stochastic systems with delay
The problem of asymptotic $ p $-stability for a linear differential equation with delay and stochastic perturbations, described by a set of mutually independent standard Wiener processes and the Poisson measure, is considered. It is shown the solution of this stability problem for some particular ca...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241560?viewType=HTML |
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| _version_ | 1846156531133841408 |
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| author | Leonid Shaikhet |
| author_facet | Leonid Shaikhet |
| author_sort | Leonid Shaikhet |
| collection | DOAJ |
| description | The problem of asymptotic $ p $-stability for a linear differential equation with delay and stochastic perturbations, described by a set of mutually independent standard Wiener processes and the Poisson measure, is considered. It is shown the solution of this stability problem for some particular cases of the considered stochastic delay differential equation. However, for the general case of the considered equation, the proposed problem remains open and is presented to the attention of potential readers. |
| format | Article |
| id | doaj-art-631eeaa5817b44c08ca9d8496581fbf4 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-631eeaa5817b44c08ca9d8496581fbf42024-11-26T01:28:05ZengAIMS PressAIMS Mathematics2473-69882024-11-01911325713257710.3934/math.20241560About one unsolved problem in asymptotic p-stability of stochastic systems with delayLeonid Shaikhet 0Department of Mathematics, Ariel University, Ariel 40700, IsraelThe problem of asymptotic $ p $-stability for a linear differential equation with delay and stochastic perturbations, described by a set of mutually independent standard Wiener processes and the Poisson measure, is considered. It is shown the solution of this stability problem for some particular cases of the considered stochastic delay differential equation. However, for the general case of the considered equation, the proposed problem remains open and is presented to the attention of potential readers.https://www.aimspress.com/article/doi/10.3934/math.20241560?viewType=HTMLstochastic perturbationswhite noisepoisson's jumpsasymptotic $ p $-stabilitystability in probabilitygeneral method of lyapunov functionals construction |
| spellingShingle | Leonid Shaikhet About one unsolved problem in asymptotic p-stability of stochastic systems with delay AIMS Mathematics stochastic perturbations white noise poisson's jumps asymptotic $ p $-stability stability in probability general method of lyapunov functionals construction |
| title | About one unsolved problem in asymptotic p-stability of stochastic systems with delay |
| title_full | About one unsolved problem in asymptotic p-stability of stochastic systems with delay |
| title_fullStr | About one unsolved problem in asymptotic p-stability of stochastic systems with delay |
| title_full_unstemmed | About one unsolved problem in asymptotic p-stability of stochastic systems with delay |
| title_short | About one unsolved problem in asymptotic p-stability of stochastic systems with delay |
| title_sort | about one unsolved problem in asymptotic p stability of stochastic systems with delay |
| topic | stochastic perturbations white noise poisson's jumps asymptotic $ p $-stability stability in probability general method of lyapunov functionals construction |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241560?viewType=HTML |
| work_keys_str_mv | AT leonidshaikhet aboutoneunsolvedprobleminasymptoticpstabilityofstochasticsystemswithdelay |