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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Main Author: Leonid Shaikhet
Format: Article
Language:English
Published: AIMS Press 2024-11-01
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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author Leonid Shaikhet
author_facet Leonid Shaikhet
author_sort Leonid Shaikhet
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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.
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issn 2473-6988
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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