Stability of delay differential equations with fading stochastic perturbations of the type of white noise and Poisson's jumps
type: Item
instance of: scholarly article
title: Stability of delay differential equations with fading stochastic perturbations of the type of white noise and Poisson's jumps
zbMATH Open document ID: 1458.34139
author: Leonid Shaikhet
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2020-08-03T00:00:00Z
review text: This paper is mainly concerned with a delay differential equation with stochastic perturbations of the type of white noise and Poisson's jumps. They prove that if the stochastic perturbations decay on the infinity quickly enough then sufficient conditions for asymptotic stability of the zero solution of the deterministic differential equation with delay imply also asymptotic mean square stability of the zero solution of the stochastic differential equation. The stability conditions are obtained via the general method of Lyapunov functionals construction and the method of Linear Matrix Inequalities (LMIs). Investigation of the situation when stochastic perturbations do not fade on the infinity or fade not enough quickly is proposed as an unsolved problem.
reviewed by: Yong Kui Chang
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K27
zbMATH DE Number: 7226746
zbMATH Keywords: stochastic delay differential equation
zbMATH Keywords: Wiener process
zbMATH Keywords: Poisson's measure
zbMATH Keywords: fading stochastic perturbations
zbMATH Keywords: asymptotic mean square stability
MaRDI profile type: Publication
full work available at URL: dcdsb.2020077
OpenAlex ID: W3001964604
cites work: Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
cites work: About stability of delay differential equations with square integrable level of stochastic perturbations
cites work: About stability of difference equations with continuous time and fading stochastic perturbations
DOI: 10.3934/DCDSB.2020077
description: scientific article; zbMATH DE number 7226746