The perturbed nonhomogeneous Markov system
The authors introduce the concept of a perturbed nonhomogeneous Markov system. Then they relax the usual basic assumption that the imbedded nonhomogeneous Markov chain converges to a homogeneous Markov chain and under this weak assumption they prove that a limiting expected population structure exists. It is found in closed analytic form as a function of parameters that uniquely determine the system. Also the sensitivity of the limiting expected population structure of a nonhomogeneous Markov system on perturbation of the limiting input probabilities is studied. The asymptotic behaviour of the variances and covariances of the class sizes of a perturbed nonhomogeneous Markov system is considered and found in a closed analytic form.
scientific article; zbMATH DE number 1331310
scientific article