The perturbed nonhomogeneous Markov system
type: Item
instance of: scholarly article
title: The perturbed nonhomogeneous Markov system
zbMATH Open document ID: 0947.60076
DOI: 10.1016/S0024-3795(98)10025-3
author: P.-C. G. Vassiliou
author: M. A. Symeonaki
published in: Linear Algebra and its Applications
publication date: 2000-11-06T00:00:00Z
review text: The authors introduce the concept of a perturbed nonhomogeneous Markov system. Then they relax the usual basic assumption that the imbedded nonhomogeneous Markov chain converges to a homogeneous Markov chain and under this weak assumption they prove that a limiting expected population structure exists. It is found in closed analytic form as a function of parameters that uniquely determine the system. Also the sensitivity of the limiting expected population structure of a nonhomogeneous Markov system on perturbation of the limiting input probabilities is studied. The asymptotic behaviour of the variances and covariances of the class sizes of a perturbed nonhomogeneous Markov system is considered and found in a closed analytic form.
Mathematics Subject Classification ID: 60J20
zbMATH DE Number: 1331310
zbMATH Keywords: perturbed nonhomogeneous Markov system
zbMATH Keywords: limiting expected population structure
zbMATH Keywords: asymptotic behaviour
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
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cites work: Interactive markov chains
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cites work: Periodicity of asymptotically attainable structures in nonhomogeneous Markov systems
cites work: Q4098444
cites work: On a problem in population structure
cites work: Limiting structures in hierarchical manpower systems
cites work: A continuous-time population model with poisson recruitment
cites work: Continuous-time stochastic models of a multigrade population
cites work: A semi-Markov model for a multigrade population with Poisson recruitment
cites work: Extending the Entropy Stability Measure for Manpower Planning
cites work: Generalized Inversion of Modified Matrices
cites work: The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
cites work: Updating finite markov chains by using techniques of group matrix inversion
cites work: Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems
cites work: Asymptotic behavior of Markov systems
cites work: Asymptotic variability of nonhomogeneous Markov systems under cyclic behaviour
cites work: Asymptotically Attainable Structures in Nonhomogeneous Markov Systems
cites work: Quasi-ergodicity for non-homogeneous continuous-time Markov chains
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description: scientific article; zbMATH DE number 1331310