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., 2016, Volume 28, Issue 3, Pages 28–48 (Mi dm1382)  

Large deviations of branching processes with immigration in random environment

D. V. Dmitrushchenkov, A. V. Shklyaev

Lomonosov Moscow State University

Abstract: We consider branching process $Z_n$ in random environment such that the associated random walk $S_n$ has increments $\xi_i$ with mean $\mu$ and satisfy the Cramér condition $\mathbf{E}e^{h\xi_i}<\infty$, $0<h<h^+$. Let $\chi_i$ be the number of particles immigrating into the $i^th$ generation of the process, $\mathbf{E}\chi_i^h<\infty$, $0<h<h^+$. We suppose that the number of offsprings of one particle conditioned on the environment has the geometric distribution. It is shown that the supplement of immigration to critical or supercritical processes results only in the change of multiplicative constant in the asymptotics of large deviation probabilities $\mathbf PŻ_n\ge \exp(\theta n)\}$, $\theta>\mu$. In the case of subcritical processes analogous result is obtained for $\theta>\gamma$, where $\gamma>0$ is some constant. For all constants explicit formulas are given.

Keywords: Large deviations, random walks, branching processes, random environments, Cramér condition, processes with immigration.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31091 мол-а
The work was supported by the RFBR grant No. 14-01-31091 mol-a.


DOI: https://doi.org/10.4213/dm1382

Full text: PDF file (577 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2017, 27:6, 361–376

Bibliographic databases:

UDC: 519.218.2
Received: 24.11.2015
Revised: 17.07.2016

Citation: D. V. Dmitrushchenkov, A. V. Shklyaev, “Large deviations of branching processes with immigration in random environment”, Diskr. Mat., 28:3 (2016), 28–48; Discrete Math. Appl., 27:6 (2017), 361–376

Citation in format AMSBIB
\Bibitem{DmiShk16}
\by D.~V.~Dmitrushchenkov, A.~V.~Shklyaev
\paper Large deviations of branching processes with immigration in random environment
\jour Diskr. Mat.
\yr 2016
\vol 28
\issue 3
\pages 28--48
\mathnet{http://mi.mathnet.ru/dm1382}
\crossref{https://doi.org/10.4213/dm1382}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3643045}
\elib{http://elibrary.ru/item.asp?id=27349812}
\transl
\jour Discrete Math. Appl.
\yr 2017
\vol 27
\issue 6
\pages 361--376
\crossref{https://doi.org/10.1515/dma-2017-0037}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000417791200003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85038389667}


Linking options:
  • http://mi.mathnet.ru/eng/dm1382
  • https://doi.org/10.4213/dm1382
  • http://mi.mathnet.ru/eng/dm/v28/i3/p28

    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:204
    Full text:6
    References:28
    First page:36

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