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, 1980, Volume 25, Issue 3, Pages 502–512 (Mi tvp1090)  

This article is cited in 4 scientific papers (total in 4 papers)

A new variant of the functional law of the iterated logarithm

A. V. Bulinskiĭ

Moscow
Full-text PDF (557 kB) Citations (4)
Abstract: The full description of the set of limit points of the sequence (3) is given, where $W(t)$ is a $d$-dimensional Brownian motion consisting of $d$ independent Brownian motions and $\varphi(\,\cdot\,)$ is arbitrary function such that $\varphi(t)\uparrow\infty$ ($t\uparrow\infty$). We show that with probability one this set coincides with the set $K_{R(\varphi)}$ specified in theorems 1–3. The sequences of the form (18) are also considered. The result of V. Strassen is a special case when $\varphi(t)=\sqrt{2\ln\ln t}$. The generalization of Hartman–Wintner's theorem is obtained. Theorems 4, 5 are valid for all sequences satisfying the almost sure invariance principles (martingale-differences, sequences with mixing etc.).
Received: 28.03.1979
English version:
Theory of Probability and its Applications, 1981, Volume 25, Issue 3, Pages 493–503
DOI: https://doi.org/10.1137/1125061
Bibliographic databases:
Language: Russian
Citation: A. V. Bulinskiǐ, “A new variant of the functional law of the iterated logarithm”, Teor. Veroyatnost. i Primenen., 25:3 (1980), 502–512; Theory Probab. Appl., 25:3 (1981), 493–503
Citation in format AMSBIB
\Bibitem{Bul80}
\by A.~V.~Bulinski{\v\i}
\paper A new variant of the functional law of the iterated logarithm
\jour Teor. Veroyatnost. i Primenen.
\yr 1980
\vol 25
\issue 3
\pages 502--512
\mathnet{http://mi.mathnet.ru/tvp1090}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=582580}
\zmath{https://zbmath.org/?q=an:0462.60035|0436.60031}
\transl
\jour Theory Probab. Appl.
\yr 1981
\vol 25
\issue 3
\pages 493--503
\crossref{https://doi.org/10.1137/1125061}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1980MB70100005}
Linking options:
  • https://www.mathnet.ru/eng/tvp1090
  • https://www.mathnet.ru/eng/tvp/v25/i3/p502
  • This publication is cited in the following 4 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
    Statistics & downloads:
    Abstract page:316
    Full-text PDF :133
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024