Geodesic
Poisson approximation for the number of long match patterns in random sequences
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 731-742

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Let $X_1 , \ldots ,X_m ,Y_1 , \ldots ,Y_n $ be independent identically distributed random variables with discrete state space. We estimate the rate of convergence in the limit theorems for the number of long match patterns and for the length of the longest match pattern in random sequences $X_1 , \ldots ,X_m ,Y_1 , \ldots ,Y_n $. The results improve the corresponding ones received by Zubkov–Mikhailov, Arratia–Gordon–Waterman, and others.
Mots-clés : Poisson approximation
Keywords: Chen–Stein method. 
@article{TVP_1994_39_4_a5,
     author = {S. Yu. Novak},
     title = {Poisson approximation for the number of long match patterns in random sequences},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {731--742},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a5/}
}
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S. Yu. Novak. Poisson approximation for the number of long match patterns in random sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 4, pp. 731-742. http://geodesic.mathdoc.fr/item/TVP_1994_39_4_a5/