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

摘要

This three-part series work investigates the qualitative analysisof large-scale stochastic hereditary systems under randomstructural perturbations. The random structural perturbations aredescribed by a Markov chain with a finite number of states. Thefirst part of this three-part series work deals with the problemformulation and the development of mathematical tool to undertakethis investigation. In this first part, we present variationalcomparison theorems for isolated subsystems of large-scalestochastic hereditary systems under Markovian structuralperturbations. This part lays down the basis for the study ofhierarchic systems.