Geodesic
Limit distributions of random variables connected with multiple long duplications in a~sequence lof independent trials
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 182-187

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Let $X_0,X_1,\dots$ be a sequence of independent trials with $m$ outcomes. We prove limit theorems for the distribution of the number of multiple long duplications \begin{gather*} ((X_{i_1}, X_{i_1+1},\dots,X_{i_1+n-1})=(X_{i_t}, X_{i_t+1},\dots,X_{i_t+n-1}) \\ t=2,\dots,k,\quad1\le i_1\dots\le N), \end{gather*} for the distribution of the waiting time until the first multiple duplication of a given length and for the distribution of the maximal duplication length. 
@article{TVP_1974_19_1_a17,
     author = {V. G. Mikhailov},
     title = {Limit distributions of random variables connected with multiple long duplications in a~sequence lof independent trials},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {182--187},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a17/}
}
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V. G. Mikhailov. Limit distributions of random variables connected with multiple long duplications in a~sequence lof independent trials. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 182-187. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a17/