Abstract
Abstract Let X 0, X 1, … be a simple ergodic Markov chain with a finite set of states and ξ̃ n, k (s) be a number of runs of k-fold repetitions of strings having length s. Estimates of accuracy of the Poisson approximation for the distribution of ξ n, k (s) in the sequence X 0, X 1, …, X n+s−1 are obtained, these estimates are uniform over k.
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