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Diskretnaya Matematika, 2021, Volume 33, Issue 3, Pages 64–78
DOI: https://doi.org/10.4213/dm1656 (Mi dm1656) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the asymptotic normality conditions for the number of repetitions in a stationary random sequence

V. G. Mikhailova, N. M. Mezhennayab, A. V. Volginc

a Steklov Mathematical Institute of Russian Academy of Sciences
b Bauman Moscow State Technical University
c MIREA — Russian Technological University
Full-text PDF (511 kB) Citations (3)
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DOI: https://doi.org/10.4213/dm1656
Abstract: We study conditions of the asymptotic normality of the number of repetitions (pairs of equal values) in a segment of strict sense stationary random sequence of values from $\{1,2,\ldots,N\}$ satisfying the strong uniform mixing condition. It is shown that under natural conditions for the number of repetitions to be asymptotically normal as the length of the segment tends to infinity it is necessary for the stationary distribution to be different from the equiprobable one. Under additional conditions the accuracy of the normal approximation in the uniform metrics is estimated.
Keywords: stationary sequence, $U$-statistics, repetitions of elements, normal approximation accuracy.
Received: 08.07.2021
English version:
Discrete Mathematics and Applications, 2022, Volume 32, Issue 6, Pages 391–401
DOI: https://doi.org/10.1515/dma-2022-0034
Bibliographic databases:
Document Type: Article
UDC: 519.214.5
Language: Russian
Citation: V. G. Mikhailov, N. M. Mezhennaya, A. V. Volgin, “On the asymptotic normality conditions for the number of repetitions in a stationary random sequence”, Diskr. Mat., 33:3 (2021), 64–78; Discrete Math. Appl., 32:6 (2022), 391–401
Citation in format AMSBIB
\Bibitem{MikMezVol21}
\by V.~G.~Mikhailov, N.~M.~Mezhennaya, A.~V.~Volgin
\paper On the asymptotic normality conditions for the number of repetitions in a stationary random sequence
\jour Diskr. Mat.
\yr 2021
\vol 33
\issue 3
\pages 64--78
\mathnet{http://mi.mathnet.ru/dm1656}
\crossref{https://doi.org/10.4213/dm1656}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4227270}
\transl
\jour Discrete Math. Appl.
\yr 2022
\vol 32
\issue 6
\pages 391--401
\crossref{https://doi.org/10.1515/dma-2022-0034}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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