STUDIES IN MARKOFF CHAINS WITH A FINITE NUMBER OF STATES

Let \left(\xi_n, n \geqslant 0\right) be an irreducible Markov Chain on the state-space \1,2, \cdots, s\ with transition probability matrix P. Denote by v_m(i=1, \cdots, s) the number of occurrences of stato i among \xi_1, \cdots, \xi_n. Let \left(q_1, \cdots, q_s\right) be the only stationary distribution for P and a_1, \cdots, a_2 be any real numbers satisfying q_1 a_1+q_2 a_2+\cdots+q_8 a_3=0. In this paper, the gonorating function of moments for v_n 1, \cdots, v_n s and the explicit oxprossions of the limiting distribations for \frac1\sqrtn \sum_1^2 i_i \gamma_a t and \left(\fracv_n 1-n q_1\sqrtn, \cdots, \fracv_n s-n q_2\sqrtn_6\right) are obtained respectively. In addition, several rolated results are given.