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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Diskr. Mat., 2019, Volume 31, Issue 3, Pages 3–16 (Mi dm1567)  

Two-boundary problem for a random walk with restriction on the maximum increment

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A random walk with zero drift and finite positive variance $\sigma ^{2}$ is considered. For positive numbers $x,y$ there is a limit of the probability that the first exit of the random walk from the interval $(-z\sigma \sqrt{n} ,y\sigma \sqrt{n})$ will occur through the left boundary and the maximum increment of the walk until this exit is less than $x\sigma \sqrt{n}$, where $x$ is a positive number. The limit theorem for the moment of the first exit of the walk from the specified interval is established, provided that this exit occurs through the left boundary and the restriction on the maximum increment is fulfills.

Keywords: random walks with zero drift, boundary problems, limit theorems.

DOI: https://doi.org/10.4213/dm1567

Full text: PDF file (457 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 519.217.31
Received: 03.03.2019

Citation: V. I. Afanasyev, “Two-boundary problem for a random walk with restriction on the maximum increment”, Diskr. Mat., 31:3 (2019), 3–16

Citation in format AMSBIB
\Bibitem{Afa19}
\by V.~I.~Afanasyev
\paper Two-boundary problem for a random walk with restriction on the maximum increment
\jour Diskr. Mat.
\yr 2019
\vol 31
\issue 3
\pages 3--16
\mathnet{http://mi.mathnet.ru/dm1567}
\crossref{https://doi.org/10.4213/dm1567}


Linking options:
  • http://mi.mathnet.ru/eng/dm1567
  • https://doi.org/10.4213/dm1567
  • http://mi.mathnet.ru/eng/dm/v31/i3/p3

    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
  • Дискретная математика
    Number of views:
    This page:58
    References:6
    First page:4

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