Geodesic
Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 67-78

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Let $X_0,X_1,\ldots$ be a simple ergodic Markov chain with a finite set of states and $\tilde\xi_{n,k}(s)$ 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 $\xi_{n,k}(s)$ in the sequence $X_0,X_1,\ldots,X_{n+s-1}$ are obtained, these estimates are uniform over $k$. \def\acknowledgementname{Funding
Keywords: Markov chain, $k$-fold repetitions of $s$-strings, accuracy of the Poisson approximation. 
@article{DM_2015_27_4_a5,
     author = {Vladimir G. Mikhaylov},
     title = {Estimates of accuracy of the {Poisson} approximation for the distribution of number of runs of long string repetitions in a {Markov} chain},
     journal = {Diskretnaya Matematika},
     pages = {67--78},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_4_a5/}
}
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Vladimir G. Mikhaylov. Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 67-78. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a5/