Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems
George M. Tsaklidis, Panagiotis C. G. Vassiliou · Journal of Applied Probability · 1988
In this paper we study the asymptotic periodicity of the sequence of means, variances and covariances of the state sizes of non-homogeneous Markov systems. It is proved that under the assumption that the sequence of the extended stochastic transition matrices converge to a matrix which is an irreducible stochastic matrix of period d , and all the matrices in this sequence have the same incidence matrix, then the sequence of means, variances and covariances splits into d subsequences which converge. Finally, we discuss the application of the present results in a manpower system.