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, 2003, Volume 48, Issue 2, Pages 321–339
DOI: https://doi.org/10.4213/tvp287 (Mi tvp287) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Lower functions of empirical processes and Brownian sheets

M. A. Lifshitsa, Zh. Shib

a University of Sciences and Technologies
b Université Pierre & Marie Curie, Paris VI
Full-text PDF (1619 kB) Citations (4)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tvp287
Abstract: We give a complete characterization of the lower functions for the two-parameter Brownian sheet and for the uniform empirical process via integral criteria. Our result for the Brownian sheet can be viewed as a solution, in a very special case (the general case remains an open question), of the following problem: find the escape rate of infinite-dimensional Brownian motion. Our result for the empirical process disproves (and provides the correct form of) a conjecture in [G. R. Shorack and J. A. Wellner, Wiley, New York, 1986.].
Keywords: rate of escape, empirical process, infinite-dimensional Brownian motion, Brownian sheet, lower function.
Received: 30.09.2002
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 2, Pages 273–287
DOI: https://doi.org/10.1137/S0040585X97980397
Bibliographic databases:
Language: Russian
Citation: M. A. Lifshits, Zh. Shi, “Lower functions of empirical processes and Brownian sheets”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 321–339; Theory Probab. Appl., 48:2 (2004), 273–287
Citation in format AMSBIB
\Bibitem{LifShi03}
\by M.~A.~Lifshits, Zh.~Shi
\paper Lower functions of empirical processes and Brownian sheets
\jour Teor. Veroyatnost. i Primenen.
\yr 2003
\vol 48
\issue 2
\pages 321--339
\mathnet{http://mi.mathnet.ru/tvp287}
\crossref{https://doi.org/10.4213/tvp287}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2015455}
\zmath{https://zbmath.org/?q=an:1058.60026}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 2
\pages 273--287
\crossref{https://doi.org/10.1137/S0040585X97980397}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000222357100006}
Linking options:
  • https://www.mathnet.ru/eng/tvp287
  • https://doi.org/10.4213/tvp287
  • https://www.mathnet.ru/eng/tvp/v48/i2/p321
    • 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:322
    Full-text PDF :153
    References:58
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024