Applied Stochastic Models and Data Analysis · 1997 · 63 citations · 0 references
EngineeringMathematicsDynamical SystemsProbability TheoryStochastic ProcessesBirth-death ProcessesMarkov ProcessesSemi-markov ProcessesStochastic Differential EquationsStochastic StabilityStochastic Systems ModelingMarkov Diffusion ProcessesNon-homogeneous Markov ModelsSemi-markov ModellingStability Of Markov ProcessesStochastic Dynamical SystemsStochastic Process Analysis
A review of the evolution of the theory of non-homogeneous Markov systems (NHMSs) is given. It starts with the definition of the stochastic process NHMS, discusses the variability of the process and provides as examples some real applications of the theory. Then, important novel ideas and basic theorems are presented on: (i) the asymptotic behaviour of NHMSs; (ii) control theory; (iii) cyclic behaviour; (iv) physics of populations: stability, entropy, energy; (v) non-homogeneous semi-Markov systems; (vi) the NHMS in a stochastic environment. © 1998 John Wiley & Sons, Ltd.