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., 1983, Volume 28, Issue 4, Pages 760–763 (Mi tvp2223)  

Short Communications

On sums of random variables with values in a Hilbert space

E. R. Vvedenskaya


Abstract: Let $H$ be a separable Hilbert space and $X1,X2,…$ be a sequence of independent random vectors identically and symmetrically distributed in $H$ such that $\mathbf P\{\|X_1\|>0\}>0$. Let $S_n=X_1+…+X_n$ and
$$ \gamma_n(\alpha)=\inf\{R: \mathbf P\{\|S_n\|\le R\}\ge\alpha\},\qquad 0<\alpha<1. $$
We prove that if $\mathbf E\|X_1\|=\infty$ then
$$ \mathbf P\{\limsup_{n\to\infty}\|S_n\|/\gamma_n(\alpha)=\infty\}=1. $$
In the finite-dimensional case the last equality is valid without any additional conditions as it follows from [4].

Full text: PDF file (270 kB)

English version:
Theory of Probability and its Applications, 1984, 28:4, 797–800

Bibliographic databases:

Received: 28.06.1983

Citation: E. R. Vvedenskaya, “On sums of random variables with values in a Hilbert space”, Teor. Veroyatnost. i Primenen., 28:4 (1983), 760–763; Theory Probab. Appl., 28:4 (1984), 797–800

Citation in format AMSBIB
\Bibitem{Vve83}
\by E.~R.~Vvedenskaya
\paper On sums of random variables with values in a~Hilbert space
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 4
\pages 760--763
\mathnet{http://mi.mathnet.ru/tvp2223}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=726901}
\zmath{https://zbmath.org/?q=an:0544.60016|0522.60009}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 4
\pages 797--800
\crossref{https://doi.org/10.1137/1128077}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TV66700013}


Linking options:
  • http://mi.mathnet.ru/eng/tvp2223
  • http://mi.mathnet.ru/eng/tvp/v28/i4/p760

    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
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:85
    Full text:49

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