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

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


Diskretnaya Matematika, 2001, Volume 13, Issue 1, Pages 132–157
DOI: https://doi.org/10.4213/dm270
(Mi dm270)
 

This article is cited in 11 scientific papers (total in 11 papers)

Limit theorems for an intermediately subcritical and a strongly subcritical branching process in a random environment

V. I. Afanasyev
References:
Abstract: Let $\{\xi_n\}$ be an intermediately subcritical branching process in a random environment with linear-fractional generating functions, and let $m_n^+$ be the conditional mathematical expectation of $\xi_n$ under the condition that the random environment is fixed and $\xi_n>0$. We establish the convergence of the sequence of processes $\{\xi_{[nt]}/m^+_{[nt]},\ t\in(0,1)\mid \xi_n>\nobreak0\}$ as $n\to\infty$ in the sense of finite-dimensional distributions. As a corollary, we establish the convergence of the sequence of processes $\{\ln\xi_{[nt]}/\ \sqrt n,\ t\in[0,1]\mid \xi_n>0\}$ in the sense of finite-dimensional distributions to a process expressed in terms of the Brownian meander.
For a strongly subcritical branching process in a random environment $\{\xi_n\}$ with linear-fractional generating functions, we establish the convergence of the sequence $\{\xi_{[nt]},\ t\in(0,1)\mid \xi_n>0\}$ in the sense of finite-dimensional distributions to a process whose all cross-sections are independent and identically distributed.
This research was supported by the Russian Foundation for Basic Research, grant 98–01–00524, and INTAS, grant 99–01317.
Received: 20.01.2000
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: V. I. Afanasyev, “Limit theorems for an intermediately subcritical and a strongly subcritical branching process in a random environment”, Diskr. Mat., 13:1 (2001), 132–157; Discrete Math. Appl., 11:2 (2001), 105–131
Citation in format AMSBIB
\Bibitem{Afa01}
\by V.~I.~Afanasyev
\paper Limit theorems for an intermediately subcritical and a strongly subcritical branching process in a random environment
\jour Diskr. Mat.
\yr 2001
\vol 13
\issue 1
\pages 132--157
\mathnet{http://mi.mathnet.ru/dm270}
\crossref{https://doi.org/10.4213/dm270}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1846044}
\zmath{https://zbmath.org/?q=an:1045.60087}
\transl
\jour Discrete Math. Appl.
\yr 2001
\vol 11
\issue 2
\pages 105--131
Linking options:
  • https://www.mathnet.ru/eng/dm270
  • https://doi.org/10.4213/dm270
  • https://www.mathnet.ru/eng/dm/v13/i1/p132
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
    Statistics & downloads:
    Abstract page:679
    Full-text PDF :243
    References:75
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024