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

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.