RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






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


Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 4, Pages 733–753 (Mi tvp127)  

On the CLT for means under the rotation action. I

M. Weber

Institut de Recherche Mathématique Avancée, Université de Strasbourg

Abstract: We propose a method allowing us to build, for various typical means generated by the action of any given irrational rotation of the circle, examples of $L^2$ functions satisfying the central limit theorem (CLT). We consider, for instance, nonlinear means, and means along the sequence of squares. In the latter case, the circle method of Hardy and Littlewood is used. We also give an example of continuous Gaussian random Fourier series with sample paths satisfying both the CLT and the almost sure CLT.

Keywords: central limit theorem, almost sure central limit theorem, irrational rotations, nonlinear averages, square averages, weighted averages, Gaussian randomization, random Fourier series, circle method.

DOI: https://doi.org/10.4213/tvp127

Full text: PDF file (1553 kB)

English version:
Theory of Probability and its Applications, 2006, 50:4, 631–649

Bibliographic databases:

Received: 10.09.2003
Revised: 29.03.2005
Language:

Citation: M. Weber, “On the CLT for means under the rotation action. I”, Teor. Veroyatnost. i Primenen., 50:4 (2005), 733–753; Theory Probab. Appl., 50:4 (2006), 631–649

Citation in format AMSBIB
\Bibitem{Web05}
\by M.~Weber
\paper On the CLT for means under the rotation action.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 2005
\vol 50
\issue 4
\pages 733--753
\mathnet{http://mi.mathnet.ru/tvp127}
\crossref{https://doi.org/10.4213/tvp127}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2331985}
\zmath{https://zbmath.org/?q=an:1110.60018}
\elib{http://elibrary.ru/item.asp?id=9157510}
\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 4
\pages 631--649
\crossref{https://doi.org/10.1137/S0040585X97982013}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243284300005}


Linking options:
  • http://mi.mathnet.ru/eng/tvp127
  • https://doi.org/10.4213/tvp127
  • http://mi.mathnet.ru/eng/tvp/v50/i4/p733

    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
    Cycle of papers
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:144
    Full text:49

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019