Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
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

Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 2, Pages 433–443
DOI: https://doi.org/10.4213/tvp67 (Mi tvp67) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

On the CLT for means under the rotation action. II

M. Weber

Institut de Recherche Mathématique Avancée, Université de Strasbourg
Full-text PDF (922 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tvp67
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–Littlewood is used. We also give an example of continuous Gaussian random Fourier series with sample paths satisfying both CLT and 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.
Received: 10.09.2003
Revised: 29.03.2005
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 2, Pages 377–387
DOI: https://doi.org/10.1137/S0040585X97982414
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. Weber, “On the CLT for means under the rotation action. II”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 433–443; Theory Probab. Appl., 51:2 (2007), 377–387
Citation in format AMSBIB
\Bibitem{Web06}
\by M.~Weber
\paper On the CLT for means under the rotation action.~II
\jour Teor. Veroyatnost. i Primenen.
\yr 2006
\vol 51
\issue 2
\pages 433--443
\mathnet{http://mi.mathnet.ru/tvp67}
\crossref{https://doi.org/10.4213/tvp67}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2324215}
\zmath{https://zbmath.org/?q=an:1122.60029}
\elib{https://elibrary.ru/item.asp?id=9242436}
\transl
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 2
\pages 377--387
\crossref{https://doi.org/10.1137/S0040585X97982414}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000248083200014}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34447564240}
Linking options:
  • https://www.mathnet.ru/eng/tvp67
  • https://doi.org/10.4213/tvp67
  • https://www.mathnet.ru/eng/tvp/v51/i2/p433
    Cycle of papers
    This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024