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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006, Article ID 19871, 11 pages
http://dx.doi.org/10.1155/JAMSA/2006/19871

Large-scale stochastic hereditary systems under Markovian structural perturbations. Part I. Variational comparison theorems

Department of Mathematics, The University of Texas at Arlington, Arlington 76019, TX, USA

Received 14 January 2005; Revised 26 October 2005; Accepted 26 October 2005

Copyright © 2006 G. S. Ladde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This three-part series work investigates the qualitative analysis of large-scale stochastic hereditary systems under random structural perturbations. The random structural perturbations are described by a Markov chain with a finite number of states. The first part of this three-part series work deals with the problem formulation and the development of mathematical tool to undertake this investigation. In this first part, we present variational comparison theorems for isolated subsystems of large-scale stochastic hereditary systems under Markovian structural perturbations. This part lays down the basis for the study of hierarchic systems.