RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2003, Volume 194, Number 3, Pages 61–82 (Mi msb721)  

This article is cited in 8 scientific papers (total in 8 papers)

Asymptotics of large deviations of Gaussian processes of Wiener type for $L^p$-functionals, $p>0$, and the hypergeometric function

V. R. Fatalov

M. V. Lomonosov Moscow State University

Abstract: A general result is obtained on exact asymptotics of the probabilities
$$ \mathsf P\{\int_0^1|\xi(t)|^p dt>u^p\} $$
as $u\to\infty$ and $p>0$ for Gaussian processes $\xi(t)$.
The general theorem is applied for the calculation of these asymptotics in the cases of the following processes: the Wiener process $w(t)$, the Brownian bridge, and the stationary Gaussian process $\eta(t):=w(t+1)-w(t)$, $t\in\mathbb R^1$.
The Laplace method in Banach spaces is used. The calculations of the constants reduce to solving an extremum problem for the action functional and studying the spectrum of a differential operator of the second order of Sturm–Liouville type.

DOI: https://doi.org/10.4213/sm721

Full text: PDF file (353 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2003, 194:3, 369–390

Bibliographic databases:

UDC: 519.2
MSC: Primary 60F10; Secondary 60G10, 60G15, 60J65
Received: 23.05.2002

Citation: V. R. Fatalov, “Asymptotics of large deviations of Gaussian processes of Wiener type for $L^p$-functionals, $p>0$, and the hypergeometric function”, Mat. Sb., 194:3 (2003), 61–82; Sb. Math., 194:3 (2003), 369–390

Citation in format AMSBIB
\Bibitem{Fat03}
\by V.~R.~Fatalov
\paper Asymptotics of large deviations of
Gaussian processes of Wiener type for $L^p$-functionals, $p>0$,
and the~hypergeometric function
\jour Mat. Sb.
\yr 2003
\vol 194
\issue 3
\pages 61--82
\mathnet{http://mi.mathnet.ru/msb721}
\crossref{https://doi.org/10.4213/sm721}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1992557}
\zmath{https://zbmath.org/?q=an:1062.60022}
\elib{http://elibrary.ru/item.asp?id=13441272}
\transl
\jour Sb. Math.
\yr 2003
\vol 194
\issue 3
\pages 369--390
\crossref{https://doi.org/10.1070/SM2003v194n03ABEH000721}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184089700004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0038103085}


Linking options:
  • http://mi.mathnet.ru/eng/msb721
  • https://doi.org/10.4213/sm721
  • http://mi.mathnet.ru/eng/msb/v194/i3/p61

    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

    This publication is cited in the following articles:
    1. V. R. Fatalov, “Large deviations for Gaussian processes in Hölder norm”, Izv. Math., 67:5 (2003), 1061–1079  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. R. Fatalov, “The Laplace method for small deviations of Gaussian processes of Wiener type”, Sb. Math., 196:4 (2005), 595–620  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Fatalov V.P., “Letter to the Editors”, Theory Probab. Appl., 51:3 (2007), 561–563  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. R. Fatalov, “Exact Asymptotics of Large Deviations of Stationary Ornstein–Uhlenbeck Processes for $L^p$-Functional, $p>0$”, Problems Inform. Transmission, 42:1 (2006), 46–63  mathnet  crossref  mathscinet  zmath  elib  elib
    5. V. R. Fatalov, “Exact Asymptotics of Distributions of Integral Functionals of the Geometric Brownian Motion and Other Related Formulas”, Problems Inform. Transmission, 43:3 (2007), 233–254  mathnet  crossref  mathscinet  zmath  isi  elib
    6. Louchard G., Janson S., “Tail estimates for the Brownian excursion area and other Brownian areas”, Electron. J. Probab., 12:58 (2007), 1600–1632  mathscinet  zmath  isi  elib
    7. V. R. Fatalov, “Exact asymptotics of Laplace-type Wiener integrals for $L^p$-functionals”, Izv. Math., 74:1 (2010), 189–216  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. FuChang Gao, XiangFeng Yang, “Upper tail probabilities of integrated Brownian motions”, Sci. China Math, 2015  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:305
    Full text:77
    References:42
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019