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The strong law of large numbers for moving average of continuous state nonhomogeneous Markov chains

In this paper, we will study the limit theorem for moving average of continuous state nonhomogeneous Markov chains. Firstly, we introduce the concept of ergodicity for continuous state homogeneous Markov chains. Meanwhile, we establish some lemmas which are the basis of the main result. Finally, we obtain the strong law of large numbers for moving average of continuous state nonhomogeneous Markov chains.