Exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching
type: Item
instance of: scholarly article
title: Exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching
zbMATH Open document ID: 1407.34101
DOI: 10.1155/2014/907982
author: Junhao Hu
author: Zhiying Xu
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We develop exponential stability of neutral stochastic functional differential equations with two-time-scale Markovian switching modeled by a continuous-time Markov chain which has a large state space. To overcome the computational effort and the complexity, we split the large-scale system into several classes and lump the states in each class into one class by the different states of changes of the subsystems; then, we give a limit system to effectively ``replace'' the large-scale system. Under suitable conditions, using the stability of the limit system as a bridge, the desired asymptotic properties of the large-scale system with Brownian motion and Poisson jump are obtained by utilizing perturbed Lyapunov function methods and Razumikhin-type criteria. Two examples are provided to demonstrate our results.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 93E15
Mathematics Subject Classification ID: 93D15
zbMATH DE Number: 7017574
Wikidata QID: Q59070625
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/907982
OpenAlex ID: W2034106359
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description: scientific article; zbMATH DE number 7017574