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



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






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


Mat. Zametki, 2006, Volume 79, Issue 4, Pages 505–521 (Mi mz2721)  

This article is cited in 13 scientific papers (total in 13 papers)

Integro-local theorems for sums of independent random vectors in the series scheme

A. A. Borovkov, A. A. Mogul'skii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Let $S(n)=\xi(1)+…+\xi(n)$ be a sum of independent random vectors $\xi(i)=\xi_{(n)}(i)$ with general distribution depending on a parameter $n$. We find sufficient conditions for the uniform version of the integro-local Stone theorem to hold for the asymptotics of the probability $\mathsf P(S(n)\in\Delta[x))$, where $\Delta[x)$ is a cube with edge $\Delta$ and vertex at a point $x$.

DOI: https://doi.org/10.4213/mzm2721

Full text: PDF file (294 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2006, 79:4, 468–482

Bibliographic databases:

UDC: 519.214
Received: 20.05.2004
Revised: 05.09.2005

Citation: A. A. Borovkov, A. A. Mogul'skii, “Integro-local theorems for sums of independent random vectors in the series scheme”, Mat. Zametki, 79:4 (2006), 505–521; Math. Notes, 79:4 (2006), 468–482

Citation in format AMSBIB
\Bibitem{BorMog06}
\by A.~A.~Borovkov, A.~A.~Mogul'skii
\paper Integro-local theorems for sums of independent random vectors in the series scheme
\jour Mat. Zametki
\yr 2006
\vol 79
\issue 4
\pages 505--521
\mathnet{http://mi.mathnet.ru/mz2721}
\crossref{https://doi.org/10.4213/mzm2721}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2251140}
\zmath{https://zbmath.org/?q=an:1114.60037}
\elib{http://elibrary.ru/item.asp?id=9210522}
\transl
\jour Math. Notes
\yr 2006
\vol 79
\issue 4
\pages 468--482
\crossref{https://doi.org/10.1007/s11006-006-0053-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000237374700019}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33646004908}


Linking options:
  • http://mi.mathnet.ru/eng/mz2721
  • https://doi.org/10.4213/mzm2721
  • http://mi.mathnet.ru/eng/mz/v79/i4/p505

    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. A. A. Borovkov, A. A. Mogul'skii, “Integro-local and integral theorems for sums of random variables with semiexponential distributions”, Siberian Math. J., 47:6 (2006), 990–1026  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. A. A. Mogul'skii, “Large deviations of the first passage time for a random walk with semiexponentially distributed jumps”, Siberian Math. J., 47:6 (2006), 1084–1101  mathnet  crossref  mathscinet  zmath  isi
    3. A. A. Borovkov, A. A. Mogul'skii, “On large and superlarge deviations for sums of independent random vectors under the Cramer condition. I”, Theory Probab. Appl., 51:2 (2007), 227–255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. A. Mogulskiǐ, Ch. Pagma, “Superlarge deviations for sums of random variables with arithmetical super-exponential distributions”, Siberian Adv. Math., 18:3 (2008), 185–208  mathnet  crossref  mathscinet
    5. A. A. Mogul'skii, “An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions”, Siberian Math. J., 49:4 (2008), 669–683  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. A. A. Borovkov, A. A. Mogul'skii, “On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. I”, Theory Probab. Appl., 53:2 (2009), 301–311  mathnet  crossref  crossref  zmath  isi
    7. A. A. Borovkov, A. A. Mogul'skii, “On Large Deviations of Sums of Independent Random Vectors on the Boundary and Outside of the Cramér Zone. II”, Theory Probab. Appl., 53:4 (2009), 573–593  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. A. Borovkov, “Integro-local and local theorems for normal and large deviations of sums of nonidentically distributed random variables in the scheme of series”, Theory Probab. Appl., 54:4 (2010), 571–587  mathnet  crossref  crossref  mathscinet  isi
    9. A. A. Mogulskii, “Integralnye i integro-lokalnye teoremy dlya summ sluchainykh velichin s semieksponentsialnymi raspredeleniyami”, Sib. elektron. matem. izv., 6 (2009), 251–271  mathnet  mathscinet  elib
    10. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Delbaen F., Kowalski E., Nikeghbali A., “Mod-Phi Convergence”, Int. Math. Res. Notices, 2015, no. 11, 3445–3485  crossref  mathscinet  zmath  isi  elib  scopus
    12. L. V. Rozovskii, “Integro-local CLT for sums of independent nonlattice random vectors”, Theory Probab. Appl., 64:1 (2019), 27–40  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. L. V. Rozovskii, “On integro-local CLT for sums of independent random vectors”, Theory Probab. Appl., 64:4 (2019), 564–578  mathnet  crossref  crossref
  • Математические заметки Mathematical Notes
    Number of views:
    This page:391
    Full text:123
    References:38
    First page:7

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