Loading [MathJax]/jax/output/CommonHTML/jax.js
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, 2008, Volume 53, Issue 2, Pages 382–390
DOI: https://doi.org/10.4213/tvp2421 (Mi tvp2421) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

On Gaussian Measure of Balls in a Hilbert Space

L. V. Rozovskii

Saint-Petersburg Chemical-Pharmaceutical Academy
Full-text PDF (936 kB) Citations (5)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tvp2421
Abstract: Let X be a centered Gaussian random vector taking values in a separable Hilbert space H, and let a∈H. We investigate the behavior of the density and the distribution function of a noncentered ball ‖X−a‖2 by means of its Laplace transform and obtain the results with an optimal estimate of the accuracy rate. As a tool we use a “local limit theorems” approach.
Keywords: small balls, Gaussian measure, Hilbert space, Laplace transform.
Received: 21.10.2003
Revised: 14.02.2008
English version:
Theory of Probability and its Applications, 2009, Volume 53, Issue 2, Pages 357–364
DOI: https://doi.org/10.1137/S0040585X97983638
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: L. V. Rozovskii, “On Gaussian Measure of Balls in a Hilbert Space”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 382–390; Theory Probab. Appl., 53:2 (2009), 357–364
Citation in format AMSBIB
\Bibitem{Roz08}
\by L.~V.~Rozovskii
\paper On Gaussian Measure of Balls in a Hilbert Space
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 2
\pages 382--390
\mathnet{http://mi.mathnet.ru/tvp2421}
\crossref{https://doi.org/10.4213/tvp2421}
\zmath{https://zbmath.org/?q=an:1191.60045}
\transl
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 2
\pages 357--364
\crossref{https://doi.org/10.1137/S0040585X97983638}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267617600016}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67249102388}
Linking options:
  • https://www.mathnet.ru/eng/tvp2421
  • https://doi.org/10.4213/tvp2421
  • https://www.mathnet.ru/eng/tvp/v53/i2/p382
    • This publication is cited in the following 5 articles:
    1. Rozovsky L.V., “Small Ball Probabilities For Certain Gaussian Random Fields”, J. Theor. Probab., 32:2 (2019), 934–949  crossref  mathscinet  zmath  isi  scopus
    2. L. V. Rozovskii, “On the exact asymptotics of small deviations of $L_2$-norm for some Gaussian random fields”, Theory Probab. Appl., 63:3 (2019), 381–392  mathnet  crossref  crossref  isi  elib
    3. V. V. Ulyanov, “On properties of polynomials in random elements”, Theory Probab. Appl., 60:2 (2016), 325–336  mathnet  crossref  crossref  mathscinet  isi  elib
    4. L. V. Rozovsky, “Small deviations of series of weighted positive random variables”, J. Math. Sci. (N. Y.), 176:2 (2011), 224–231  mathnet  crossref
    5. Shiryaeva T.A., “Verkhnyaya otsenka veroyatnosti nakhozhdeniya gilbertovoi sluchainoi funktsii v zadannoi oblasti”, Vestn. Sibirskogo gos. aerokosmicheskogo un-ta im. akademika M. F. Reshetneva, 2009, no. 2, 45–46
    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:531
    Full-text PDF :200
    References:86
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025