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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 2, Pages 350–357
DOI: https://doi.org/10.4213/tvp3654 (Mi tvp3654) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

Poisson-type limit theorems for the number of incomplete matches of $s$-patterns

V. G. Mikhailov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (901 kB) Citations (3)
DOI: https://doi.org/10.4213/tvp3654
Abstract: 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.
Received: 05.07.1999
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 2, Pages 343–351
DOI: https://doi.org/10.1137/S0040585X97979706
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. G. Mikhailov, “Poisson-type limit theorems for the number of incomplete matches of $s$-patterns”, Teor. Veroyatnost. i Primenen., 47:2 (2002), 350–357; Theory Probab. Appl., 47:2 (2003), 343–351
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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  • https://www.mathnet.ru/eng/tvp/v47/i2/p350
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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