The perturbed nonhomogeneous Markov system

AbstractIn this paper we introduce for the first time the concept of a perturbed nonhomogeneous Markov system (P-NHMS). The expected population structure is found and its asymptotic behavior is provided under more realistic assumptions than previous studies, by relaxing the assumption that the imbedded nonhomogeneous Markov chain of a NHMS is converging to a homogeneous Markov chain. Also we study the sensitivity of the limiting expected structure on perturbations of the limiting input probabilities for a NHMS. Moreover, the asymptotic behavior of the variances and covariances of the class sizes of a P-NHMS is considered and found in an elegant closed analytic form