Abstract：The strong limit theorem of asymptotic circular Markov chains is studied. The definition of asymptotic circular Markov chains is introduced. By applying the limit property for dual functions of nonhomogeneous Markov chains, the strong limit theorem on the frequencies of occurrence of states for asymptotic circular Markov chains is established. Finally, the strong law of large numbers on the frequencies of occurrence of states for asymptotic circular Markov chains is obtained. As corollaries, the strong law of large numbers on the frequencies of occurrence of states for circular Markov chains is obtained.
2011, Vol. 32 
