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《Chinese Journal of Applied Probability and Statistics》 1990-04
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STUDIES IN MARKOFF CHAINS WITH A FINITE NUMBER OF STATES

HSU PAOLU (Peking University, Beijing)  
Let (ζ_n, n≥0) be an irreducible Marker Chain on the state-space {1, 2, ..., s} with transition probability matrix P. Denote by ν_(ni)(i=1, ..., s) the number of occurrences of state i among ζ_1, …, ζ_n. Let (q_1, …, q_n)be the only stationary distribution for P and a_1, ..., a_s be any real numbers satisfying q_1a_1+q_2a_2+…+q_sa_s=0. In this paper, the generating function of moments for ν_(n1), …, ν_(ns) and the explicit expressions of the limiting distributions for 1/n~(1/2)sum from n=1 to s a_iν_(ni) and ((ν_(n1)-nq_1)/n~(1/2), …, (ν_(ns)-nq_s)/n~(1/2)) are obtained respectively. In addition, several related results are given,
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