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Diskretnaya Matematika, 2000, Volume 12, Issue 3, Pages 49–59
DOI: https://doi.org/10.4213/dm345
(Mi dm345)
 

This article is cited in 3 scientific papers (total in 3 papers)

Repetitions of the values of a function of segments of a sequence of independent trials

A. M. Shoitov
Full-text PDF (790 kB) Citations (3)
References:
Abstract: We consider the problem on the number $\xi(N)$ of $k$-fold matchings of symbols that occur in a sequence of random variables resulting from aggregating the states of a Markov–Bruns chain generated by $n$-tuples $(X_i,\dots,X_{i+n-1})$ consisting of elements of the sequence $(X_1,\dots,X_{N+n-1})$ of independent realisations of a random variable $X$. The aggregation of states consists of applying a given function $f$, which takes a finite number of values, to the $n$-tuples $(X_i,\dots,X_{i+n-1})$. We prove a theorem on convergence to a multivariate normal law for the joint distribution of $\xi(N)$ under various aggregation functions, and give sufficient conditions on convergence of the distribution of $\xi(N)$ to the chi-square law as $N\to\infty$. These results are applied to the problem on $k$-fold imperfect matchings of $n$-tuples in a sequence of polynomial trials. In particular, we prove a theorem on convergence to a multivariate normal law for the vector of numbers of $k$-fold imperfect matchings of various lengths and ranks.
Received: 15.02.2000
Bibliographic databases:
UDC: 519.2
Language: Russian
Citation: A. M. Shoitov, “Repetitions of the values of a function of segments of a sequence of independent trials”, Diskr. Mat., 12:3 (2000), 49–59; Discrete Math. Appl., 10:4 (2000), 379–389
Citation in format AMSBIB
\Bibitem{Sho00}
\by A.~M.~Shoitov
\paper Repetitions of the values of a function of segments of a sequence of independent trials
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 3
\pages 49--59
\mathnet{http://mi.mathnet.ru/dm345}
\crossref{https://doi.org/10.4213/dm345}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810953}
\zmath{https://zbmath.org/?q=an:0974.60016}
\transl
\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 4
\pages 379--389
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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