RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Probl. Peredachi Inf.:
Year:
Volume:
Issue:
Page:
Find






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


Probl. Peredachi Inf., 2007, Volume 43, Issue 3, Pages 75–96 (Mi ppi20)  

This article is cited in 2 scientific papers (total in 2 papers)

Large Systems

Exact Asymptotics of Distributions of Integral Functionals of the Geometric Brownian Motion and Other Related Formulas

V. R. Fatalov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove results on exact asymptotics of the probabilities
$$ \mathbf P\{\int\limits_0^1e^{\varepsilon\xi(t)} dt>b\},\qquad \mathbf P\{\int\limits_0^1e^{|\varepsilon\xi(t)|} dt>b\},\qquad \varepsilon\to0, $$
where $b>1$, for two Gaussian processes $\xi(t)$, namely, a Wiener process and a Brownian bridge. We use the Laplace method for Gaussian measures in Banach spaces. Evaluation of constants is reduced to solving an extreme value problem for the rate function and studying the spectrum of a second-order differential operator of the Sturm–Liouville type with the use of Legendre functions.

Full text: PDF file (2097 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2007, 43:3, 233–254

Bibliographic databases:

UDC: 621.391.1:519.2
Received: 01.03.2007

Citation: V. R. Fatalov, “Exact Asymptotics of Distributions of Integral Functionals of the Geometric Brownian Motion and Other Related Formulas”, Probl. Peredachi Inf., 43:3 (2007), 75–96; Problems Inform. Transmission, 43:3 (2007), 233–254

Citation in format AMSBIB
\Bibitem{Fat07}
\by V.~R.~Fatalov
\paper Exact Asymptotics of Distributions of Integral Functionals of the Geometric Brownian Motion and Other Related Formulas
\jour Probl. Peredachi Inf.
\yr 2007
\vol 43
\issue 3
\pages 75--96
\mathnet{http://mi.mathnet.ru/ppi20}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2360019}
\zmath{https://zbmath.org/?q=an:1136.60357}
\elib{http://elibrary.ru/item.asp?id=13544159}
\transl
\jour Problems Inform. Transmission
\yr 2007
\vol 43
\issue 3
\pages 233--254
\crossref{https://doi.org/10.1134/S0032946007030064}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255782800006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35848957680}


Linking options:
  • http://mi.mathnet.ru/eng/ppi20
  • http://mi.mathnet.ru/eng/ppi/v43/i3/p75

    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, “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
    2. V. R. Fatalov, “Integral Functionals for the Exponential of the Wiener Process and the Brownian Bridge: Exact Asymptotics and Legendre Functions”, Math. Notes, 92:1 (2012), 79–98  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Проблемы передачи информации Problems of Information Transmission
    Number of views:
    This page:339
    Full text:69
    References:35
    First page:4

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