Geodesic
Poisson-type limit theorems for the number of incomplete matches of $s$-patterns
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 350-357

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The principal result of the paper is a limit theorem for the vector of incomplete matches (with a given number of mismatches) of $s$-patterns in two sequences of independent identically distributed random variables. The form of the joint limiting distribution is described and sufficient convergence conditions are given. Explicit estimates of the closeness to an accompanying multivariate compound Poisson distribution are obtained. The proof is based on a local version of the Chen–Stein method to evaluate the accuracy of the Poisson approximation for the distribution of a tuple of dependent random indicators.
Keywords: matches and repetitions of patterns, incomplete matches, limit compound Poisson distribution, explicit estimates of the convergence rate, Chen–Stein method. 
@article{TVP_2002_47_2_a10,
     author = {V. G. Mikhailov},
     title = {Poisson-type limit theorems for the number of incomplete matches of $s$-patterns},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {350--357},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a10/}
}
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V. G. Mikhailov. Poisson-type limit theorems for the number of incomplete matches of $s$-patterns. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 2, pp. 350-357. http://geodesic.mathdoc.fr/item/TVP_2002_47_2_a10/