Diskretnaya Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Diskr. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Diskr. Mat., 2015, Volume 27, Issue 4, Pages 141–149 (Mi dm1353)  

This article is cited in 2 scientific papers (total in 2 papers)

On the asymptotic normality of some sums of dependent random variables

M. I. Tikhomirovaa, V. P. Chistyakovb

a Academy of Cryptography of Russian Federation
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A theorem on the asymptotic normality of the sum of dependent random variables is stated and proved. Conditions of the theorem are formulated in terms of a dependency graph which characterizes the relationships between random variables. This theorem is used to prove the asymptotic normality of the sum of functions defined on subsets of elements of the stationary sequence satisfying the strong mixing condition. As an illustration of possible applications of these theorems we give a theorem on the asymptotic normality of the number of empty cells if the random sequence of cells occupied by particles is a stationary sequence satisfying the uniform strong mixing condition.

Keywords: sums of dependent variables, asymptotic normality, dependency graph, strong mixing condition.

DOI: https://doi.org/10.4213/dm1353

Full text: PDF file (443 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2017, 27:2, 123–129

Bibliographic databases:

UDC: 519.214.5
Received: 12.01.2015

Citation: M. I. Tikhomirova, V. P. Chistyakov, “On the asymptotic normality of some sums of dependent random variables”, Diskr. Mat., 27:4 (2015), 141–149; Discrete Math. Appl., 27:2 (2017), 123–129

Citation in format AMSBIB
\Bibitem{TikChi15}
\by M.~I.~Tikhomirova, V.~P.~Chistyakov
\paper On the asymptotic normality of some sums of dependent random variables
\jour Diskr. Mat.
\yr 2015
\vol 27
\issue 4
\pages 141--149
\mathnet{http://mi.mathnet.ru/dm1353}
\crossref{https://doi.org/10.4213/dm1353}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3497378}
\elib{https://elibrary.ru/item.asp?id=24849946}
\transl
\jour Discrete Math. Appl.
\yr 2017
\vol 27
\issue 2
\pages 123--129
\crossref{https://doi.org/10.1515/dma-2017-0015}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403472300008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018407959}


Linking options:
  • http://mi.mathnet.ru/eng/dm1353
  • https://doi.org/10.4213/dm1353
  • http://mi.mathnet.ru/eng/dm/v27/i4/p141

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Mikhailov, N. M. Mezhennaya, “Normal approximation for $U$- and $V$-statistics of a stationary absolutely regular sequence”, Sib. elektron. matem. izv., 17 (2020), 672–682  mathnet  crossref
    2. V. G. Mikhailov, N. M. Mezhennaya, A. V. Volgin, “Ob usloviyakh asimptoticheskoi normalnosti chisla povtorenii v statsionarnoi sluchainoi posledovatelnosti”, Diskret. matem., 33:3 (2021), 64–78  mathnet  crossref
  • Дискретная математика
    Number of views:
    This page:254
    Full text:109
    References:23
    First page:29

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021