Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space
type: Item
instance of: scholarly article
title: Average and diffusion approximation of stochastic evolutionary systems in an asymptotic split state space
zbMATH Open document ID: 1041.60061
author: V. S. Korolyuk
author: N. Limnios
published in: The Annals of Applied Probability
publication date: 2004-06-10T00:00:00Z
review text: This is a new advance in the authors' study of average and diffusion approximation of stochastic evolutionary systems. A first process \(x^{\varepsilon}\) (\(\varepsilon\) is a small parameter) takes values in \(\{0\}\cup E\) where \(\{0\}\) is an absorbing state and \(E\) is a compact space splitted into a finite number of subspaces. It is a nonergodic jump Markov process and the switched stochastic evolutionary system process has \(R^d\)-valued locally independent increments that depend on the switching process \(x^{\varepsilon}\). The three level stochastic systems considered, that is the switching process, the switched process and additive functionals such as the reward of operating time, all depend upon the parameter \(\varepsilon\). The average and diffusion approximation limit theorems are established in both simple and double merging. Particular cases and examples are presented, including stochastic integral functionals, dynamical systems, storage jump processes and compound Poisson processes.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60G46
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 2072706
zbMATH Keywords: stochastic evolutionary system
zbMATH Keywords: Markov process with locally independent increments
zbMATH Keywords: diffusion approximation
zbMATH Keywords: split state space
zbMATH Keywords: dynamic reliability
zbMATH Keywords: reward
reviewed by: Dominique Lépingle
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1075828059
OpenAlex ID: W2065983943
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DOI: 10.1214/AOAP/1075828059
description: scientific article; zbMATH DE number 2072706