RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 4, Pages 69–102 (Mi izv690)  

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

Occupation times and exact asymptotics of small deviations of Bessel processes for $L^p$-norms with $p>0$

V. R. Fatalov

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

Abstract: We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the $L^p$-norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for $p=2$ and $p=1$. We also solve extremal problems for the action functional.

DOI: https://doi.org/10.4213/im690

Full text: PDF file (737 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2007, 71:4, 721–752

Bibliographic databases:

UDC: 519.2
MSC: 60B11, 60B12, 60F05, 60G15, 60G17, 60G60
Received: 13.07.2004
Revised: 13.04.2006

Citation: V. R. Fatalov, “Occupation times and exact asymptotics of small deviations of Bessel processes for $L^p$-norms with $p>0$”, Izv. RAN. Ser. Mat., 71:4 (2007), 69–102; Izv. Math., 71:4 (2007), 721–752

Citation in format AMSBIB
\Bibitem{Fat07}
\by V.~R.~Fatalov
\paper Occupation times and exact asymptotics of small deviations of Bessel processes for
$L^p$-norms with $p>0$
\jour Izv. RAN. Ser. Mat.
\yr 2007
\vol 71
\issue 4
\pages 69--102
\mathnet{http://mi.mathnet.ru/izv690}
\crossref{https://doi.org/10.4213/im690}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2360007}
\zmath{https://zbmath.org/?q=an:1143.60052}
\elib{https://elibrary.ru/item.asp?id=9564923}
\transl
\jour Izv. Math.
\yr 2007
\vol 71
\issue 4
\pages 721--752
\crossref{https://doi.org/10.1070/IM2007v071n04ABEH002373}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000250438300003}
\elib{https://elibrary.ru/item.asp?id=13559488}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-35748939985}


Linking options:
  • http://mi.mathnet.ru/eng/izv690
  • https://doi.org/10.4213/im690
  • http://mi.mathnet.ru/eng/izv/v71/i4/p69

    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 Small Deviations for a Stationary Ornstein–Uhlenbeck Process and Some Gaussian Diffusion Processes in the $L_p$-Norm, $2\le p\le\infty$”, Problems Inform. Transmission, 44:2 (2008), 138–155  mathnet  crossref  mathscinet  isi  elib
    2. 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
    3. V. R. Fatalov, “Small deviations for two classes of Gaussian stationary processes and $L^p$-functionals, $0<p\le\infty$”, Problems Inform. Transmission, 46:1 (2010), 62–85  mathnet  crossref  mathscinet  isi
    4. V. R. Fatalov, “Large deviations for distributions of sums of random variables: Markov chain method”, Problems Inform. Transmission, 46:2 (2010), 160–183  mathnet  crossref  mathscinet  isi  elib
    5. V. R. Fatalov, “Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method”, Izv. Math., 75:4 (2011), 837–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Ya. Yu. Nikitin, R. S. Pusev, “The exact asymptotic of small deviations for a series of Brownian functionals”, Theory Probab. Appl., 57:1 (2013), 60–81  mathnet  crossref  crossref  zmath  isi  elib  elib
    7. V. R. Fatalov, “Ergodic means for large values of $T$ and exact asymptotics of small deviations for a multi-dimensional Wiener process”, Izv. Math., 77:6 (2013), 1224–1259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. V. R. Fatalov, “Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for $L^p$-functionals”, Izv. Math., 82:2 (2018), 377–406  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:379
    Full text:101
    References:37
    First page:4

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