Ergodic behavior of a Markov chain model in a stochastic environment

Abstract.

This paper is concerned with the asymptotic behavior of a time dependent Markov model in a stochastic environment, with special relevance to manpower systems. The stochastic concept is established through the notion of optional scenarios applied on the transition process. A theorem is provided for the existence and determination of the limiting structure of the means, variances and covariances of numbers in the classes of the system. It is also proved that, under certain conditions, the rate of convergence is geometric.