Periodicity of asymptotically attainable structures in nonhomogeneous Markov systems

AbstractWe find the sets of d-periodic asymptotically attainable structures, and we establish the periodicities that exist between these structures, for a nonhomogeneous Markov system in the case where the imbedded nonhomogeneous Markov chain is periodic with period d. Also, it is proved that under certain conditions each converging subsequence of the sequence of relative structures has a geometric rate of convergence