Geodesic
On the number of repetitions in Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 557-560

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The main result of the paper is contained in equations (4), (9) and (10) giving a uniform estimate for $|1-\exp(-x)-F_N(x)|$ where $F_N(x)$ is the distribution function of $\nu/M\nu$ and $\nu$ is the period between two successive repetitions of a given collection of the length $N$ of states of a Markov chain. 
@article{TVP_1965_10_3_a17,
     author = {S. A. Ivankov},
     title = {On the number of repetitions in {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {557--560},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a17/}
}
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S. A. Ivankov. On the number of repetitions in Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 557-560. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a17/