Geodesic
Poisson approximation for the number of non-decreasing runs in Markov chains
Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 2, pp. 103-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let a sequence $X_1, X_2, \dots, X_n$ be a segment of a stationary irreducible and aperiodic Markov chain with state space $\mathcal{A} = \{1,\dots, N\}$, $N \geqslant 2$. We study the non-overlapping appearances of non-decreasing runs in the sequence $X_1, X_2, \dots, X_n$. By means of Stein method we estimate the total variation distance between the distribution of the number of non-overlapping appearances of non-decreasing monotone runs and the Poisson distribution. As a corollary we prove corresponding limit theorem. 
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A. A. Minakov. Poisson approximation for the number of non-decreasing runs in Markov chains. Matematičeskie voprosy kriptografii, Tome 9 (2018) no. 2, pp. 103-116. http://geodesic.mathdoc.fr/item/MVK_2018_9_2_a8/

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