Almost sure exponential stability of hybrid stochastic functional differential equations
type: Item
instance of: scholarly article
title: Almost sure exponential stability of hybrid stochastic functional differential equations
zbMATH Open document ID: 1380.34121
author: Minghui Song
author: Xuerong Mao
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-11-28T00:00:00Z
review text: This paper is concerned with almost sure exponential stability of an \(n\)-dimensional nonlinear hybrid stochastic functional differential equation (SFDE) modelled by a Markov chain. Under Lipschitz condition, the authors show that if the corresponding hybrid SDE is almost surely exponentially stable, then there exists a positive number \(\tau^*\) such that the SFDE is also almost surely exponentially stable if \(\tau<\tau^*\). They also describe a method to determine \(\tau^*\) which can be computed numerically. Several special classes of hybrid SFDEs are discussed.
reviewed by: Xiaohu Wang
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 6813459
zbMATH Keywords: stability
zbMATH Keywords: hybrid stochastic differential functional equations
zbMATH Keywords: Itô formula
zbMATH Keywords: Brownian motion
zbMATH Keywords: Markov chain
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.10.042
OpenAlex ID: W2766861893
Wikidata QID: Q115570324
cites work: Stochastic stabilisation of functional differential equations
cites work: Q4404205
cites work: Stabilization of Linear Systems by Noise
cites work: Stochastic Equations in Infinite Dimensions
cites work: Q4086525
cites work: Almost Sure Exponential Stability of Stochastic Differential Delay Equations
cites work: Stability of regime-switching stochastic differential equations
cites work: Q3137918
cites work: Random differential inequalities
cites work: Q3999821
cites work: Q4303533
cites work: Stochastic stabilization and destabilization
cites work: Stability of stochastic differential equations with Markovian switching
cites work: Q5429735
cites work: Stabilisation of hybrid stochastic differential equations by delay feedback control
cites work: Stabilization and destabilization of hybrid systems of stochastic differential equations
cites work: Stochastic Differential Equations with Markovian Switching
cites work: Lyapunov exponents of linear stochastic functional differential equations. II: Examples and case studies
cites work: Stabilization and Destabilization by Noise in the Plane
cites work: EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS
cites work: Q4693053
DOI: 10.1016/J.JMAA.2017.10.042
description: scientific article; zbMATH DE number 6813459