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., 2008, Volume 20, Issue 1, Pages 38–51 (Mi dm987)  

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

The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain

I. A. Kruglov


Abstract: In this paper we study the weak convergence of distributions for products of random variables with values in a compact group provided that the distributions of the factors are defined by a finite simple homogeneous irreducible Markov chain. We show that after an appropriate shift the sequence of distributions of these products converges weakly to the normalised Haar measure on some closed subgroup of the initial group, in other words, the convergence principle due to B. M. Kloss holds true, which has been established earlier for products of independent factors. We describe conditions on the Markov chain and on the initial distributions which guarantee that the limit behaviour of the distribution of the products is similar to the limit behaviour of the distributions of some products of independent random variables.

DOI: https://doi.org/10.4213/dm987

Full text: PDF file (173 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2008, 18:1, 41–55

Bibliographic databases:

UDC: 519.2
Received: 30.03.2007

Citation: I. A. Kruglov, “The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain”, Diskr. Mat., 20:1 (2008), 38–51; Discrete Math. Appl., 18:1 (2008), 41–55

Citation in format AMSBIB
\Bibitem{Kru08}
\by I.~A.~Kruglov
\paper The Kloss convergence principle for products of random variables with values in a~compact group and distributions determined by a~Markov chain
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 1
\pages 38--51
\mathnet{http://mi.mathnet.ru/dm987}
\crossref{https://doi.org/10.4213/dm987}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2420495}
\zmath{https://zbmath.org/?q=an:1191.60010}
\elib{http://elibrary.ru/item.asp?id=10335647}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 1
\pages 41--55
\crossref{https://doi.org/10.1515/DMA.2008.003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-64549156007}


Linking options:
  • http://mi.mathnet.ru/eng/dm987
  • https://doi.org/10.4213/dm987
  • http://mi.mathnet.ru/eng/dm/v20/i1/p38

    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. I. A. Kruglov, “Usloviya predelnoi ravnoveroyatnosti sostoyanii registrov sdviga”, Matem. vopr. kriptogr., 1:2 (2010), 19–29  mathnet  crossref
    2. I. A. Kruglov, “Otsenka skorosti skhodimosti k ravnomernomu raspredeleniyu dlya proizvedenii elementov konechnoi gruppy, upravlyaemykh tsepyu Markova”, Matem. vopr. kriptogr., 5:1 (2014), 85–94  mathnet  crossref
    3. I. A. Kruglov, “On the completely indecomposable nonnegative matrices and A. N. Kolmogorov's condition”, J. Math. Sci., 223:5 (2017), 602–605  mathnet  crossref  mathscinet  elib
  • Дискретная математика
    Number of views:
    This page:390
    Full text:96
    References:73
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020