Geodesic
On the probability of the non-appearence of a given number of $s$-tuples in compound Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 547-551 
P. F. Belyaev. On the probability of the non-appearence of a given number of $s$-tuples in compound Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 547-551. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a15/
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     author = {P. F. Belyaev},
     title = {On the probability of the non-appearence of a~given number of $s$-tuples in compound {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {547--551},
     year = {1965},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{j_r\}$, $r=\overline{1,n}$, $j_r=\overline{1,k}$ be a sequence obtained by realizations of $n$ trials which are bound into a compound Markov chain of order $s$ with $k$ outcomes. Let $s$-tuple denote a subsequence of $\{j_r\}$ consisting of $s$ consecutive symbols and let $P(n,k;m)$ be the probability that in the sequence $\{j_r\}$ of all possible $k^s$ $s$-tuples exactly $m$ $s$-tuples are missing. The asymptotic behaviour of the probability $P(n,k;m)$ as $n\to\infty$; $k\to\infty$; $k^re^{-n/k^s} is considered.