Stability of hybrid stochastic delay systems whose discrete components have a large state space: a two-time-scale approach
type: Item
instance of: scholarly article
title: Stability of hybrid stochastic delay systems whose discrete components have a large state space: a two-time-scale approach
zbMATH Open document ID: 1200.93136
author: Chenggui Yuan
author: G. Yin
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-05-19T00:00:00Z
review text: The Itô delay stochastic differential equation \(dx(t)=f(x(t),x(t-\tau),r(t))\,dt+g(x(t),x(t-\tau),r(t))\,dW(t)\) on \(\mathbb R^n\) with \(t\mapsto r(t)\) a Markov chain on a large finite state space \(S\), independent of the Wiener process \(W\), and \(f(0,0,r)=g(0,0,r)=0\) for all \(r\in S\) is considered. Assuming the state space \(S\) to be decomposable into subsets such that changes of \(r\) between these subsets occur only rarely one may consider a Markov chain on a smaller state space as a limiting case. Conditions are given for \(p\)th moment exponential stability of the limiting system to imply the same sort of stability for the original system. Furthermore, almost sure stability and stability in distribution are discussed.
reviewed by: Hans Crauel
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 5710072
zbMATH Keywords: two-time scale
zbMATH Keywords: large state space Markov chain
zbMATH Keywords: regime switching
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.02.053
OpenAlex ID: W1965606396
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DOI: 10.1016/J.JMAA.2010.02.053
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description: scientific article; zbMATH DE number 5710072