Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






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


Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 3, Pages 417–430 (Mi tvp5192)  

This article is cited in 4 scientific papers (total in 4 papers)

Two-boundary problem for a random walk in a random environment

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Given a sequence of independent identically distributed pairs of random variables $(p_i,q_i)$, $i\in\mathbf{Z}$, with $p_0+q_0=1$, and $p_0>0$ a.s., $q_0>0$ a.s., one considers a random walk in the random environment $(p_i,q_i)$, $i\in\mathbf{Z}$. This means that, for a fixed random environment, a walking particle transits from the state $i$ either to the state $(i+1)$ with probability $p_i$ or to the state $(i-1)$ with probability $q_i$. It is assumed that $\mathbf{E}\ln (p_0/q_0)=0$, that is, the walk is oscillating. We are concerned with the exit problem of the walk under consideration from the interval $(-\lfloor an\rfloor,\lfloor bn\rfloor)$, where $a$$b$ are arbitrary positive constants. We find the asymptotics of the exit probability of the walk from the above interval from the right (the left). A limit theorem for the exit time of the walk from this interval is obtained.

Keywords: random walk in random environment, branching process in random environment with immigration, limit theorem.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01
This work was supported by the program “Dynamical systems and control theory” of the Presidium of RAS (grant PRAS-18-01).


DOI: https://doi.org/10.4213/tvp5192

Full text: PDF file (480 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2019, 63:3, 339–350

Bibliographic databases:

Received: 19.11.2017
Revised: 21.02.2018
Accepted:06.03.2018

Citation: V. I. Afanasyev, “Two-boundary problem for a random walk in a random environment”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 417–430; Theory Probab. Appl., 63:3 (2019), 339–350

Citation in format AMSBIB
\Bibitem{Afa18}
\by V.~I.~Afanasyev
\paper Two-boundary problem for a random walk in a random environment
\jour Teor. Veroyatnost. i Primenen.
\yr 2018
\vol 63
\issue 3
\pages 417--430
\mathnet{http://mi.mathnet.ru/tvp5192}
\crossref{https://doi.org/10.4213/tvp5192}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3833090}
\elib{https://elibrary.ru/item.asp?id=35276549}
\transl
\jour Theory Probab. Appl.
\yr 2019
\vol 63
\issue 3
\pages 339--350
\crossref{https://doi.org/10.1137/S0040585X97T98909X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000457753200001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064684530}


Linking options:
  • http://mi.mathnet.ru/eng/tvp5192
  • https://doi.org/10.4213/tvp5192
  • http://mi.mathnet.ru/eng/tvp/v63/i3/p417

    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

    Related presentations:

    This publication is cited in the following articles:
    1. Smadi Ch., Vatutin V., “Critical Branching Processes in Random Environment With Immigration: Survival of a Single Family”, Extremes  crossref  isi  scopus
    2. “Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. I. Afanasyev, “On the times of attaining high levels by a random walk in a random environment”, Theory Probab. Appl., 65:3 (2020), 359–374  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. A. Vatutin, E. E. D'yakonova, “Subcritical branching processes in random environment with immigration: Survival of a single family”, Theory Probab. Appl., 65:4 (2021), 527–544  mathnet  crossref  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:351
    Full text:18
    References:29
    First page:17

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021