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., 2006, Volume 51, Issue 2, Pages 385–391 (Mi tvp61)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

Limit theorems for a model of interacting two-types particles generalizing the Bartlett–McKendrick epidemic process

M. Mirzaev, A. N. Startsev

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: he present paper is a continuation of [A. N. Startsev, Theory Probab. Appl., 46 (2002), pp. 431–447] in which limit theorems are established for the number of particles changing their types to the terminal moment of the process given that the initial numbers of particles of both types tend to infinity. Here this problem is solved under the conditions that the initial number of particles having “energy” is fixed. This assumption leads to models more actual for applications, in particular, in epidemiology. A part of the obtained results (Theorems 1 and 2) has been announced in [M. Mirzaev and A. N. Startsev, Proceedings of the International ConferenceAdvances in Statistical Inferential Methods” (Almaty, 2003), NITS “Fylym,” Almaty, 2003, pp. 81–85].

Keywords: interaction of particles, non-Markovian models, number of particles changing types, limit theorems.

DOI: https://doi.org/10.4213/tvp61

Full text: PDF file (780 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2007, 51:2, 362–367

Bibliographic databases:

Received: 02.08.2004
Revised: 27.05.2005

Citation: M. Mirzaev, A. N. Startsev, “Limit theorems for a model of interacting two-types particles generalizing the Bartlett–McKendrick epidemic process”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 385–391; Theory Probab. Appl., 51:2 (2007), 362–367

Citation in format AMSBIB
\Bibitem{MirSta06}
\by M.~Mirzaev, A.~N.~Startsev
\paper Limit theorems for a model of interacting two-types particles generalizing the Bartlett--McKendrick epidemic process
\jour Teor. Veroyatnost. i Primenen.
\yr 2006
\vol 51
\issue 2
\pages 385--391
\mathnet{http://mi.mathnet.ru/tvp61}
\crossref{https://doi.org/10.4213/tvp61}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2324209}
\zmath{https://zbmath.org/?q=an:1122.60088}
\elib{https://elibrary.ru/item.asp?id=9242430}
\transl
\jour Theory Probab. Appl.
\yr 2007
\vol 51
\issue 2
\pages 362--367
\crossref{https://doi.org/10.1137/S0040585X97982360}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000248083200012}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34447575806}


Linking options:
  • http://mi.mathnet.ru/eng/tvp61
  • https://doi.org/10.4213/tvp61
  • http://mi.mathnet.ru/eng/tvp/v51/i2/p385

    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. V. Mastikhin, “Final probabilities for Becker epidemic Markov processes”, Theory Probab. Appl., 56:3 (2011), 521–527  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Sh. K. Formanov, A. N. Startsev, S. S. Sedov, “Limit theorems for the generalized size of epidemic in a Markov model with immunization”, Discrete Math. Appl., 24:2 (2014), 73–82  mathnet  crossref  crossref  mathscinet  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:326
    Full text:127
    References:63

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