RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Mat. Sb. (N.S.), 1977, Volume 103(145), Number 2(6), Pages 253–264 (Mi msb2807)  

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

Limit theorems for critical Markov branching processes with several types of particles and infinite second moments

V. A. Vatutin


Abstract: In this paper a necessary and sufficient condition is obtained for the existence of a proper limit distribution, not concentrated at one point, of the number of particles in a critical Markov branching process with several types of particles on the set of nondegenerate trajectories under the classical normalization. In the case where the limit distribution in question exists, limit distributions for the distance to the nearest common ancestor are obtained.
Bibliography: 10 titles.

Full text: PDF file (930 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1977, 32:2, 215–225

Bibliographic databases:

UDC: 519.2
MSC: 60J80, 60F05
Received: 25.11.1976

Citation: V. A. Vatutin, “Limit theorems for critical Markov branching processes with several types of particles and infinite second moments”, Mat. Sb. (N.S.), 103(145):2(6) (1977), 253–264; Math. USSR-Sb., 32:2 (1977), 215–225

Citation in format AMSBIB
\Bibitem{Vat77}
\by V.~A.~Vatutin
\paper Limit theorems for critical Markov branching processes with several types of particles and infinite second moments
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 103(145)
\issue 2(6)
\pages 253--264
\mathnet{http://mi.mathnet.ru/msb2807}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=443115}
\zmath{https://zbmath.org/?q=an:0365.60079|0396.60072}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 2
\pages 215--225
\crossref{https://doi.org/10.1070/SM1977v032n02ABEH002379}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977GH22400003}


Linking options:
  • http://mi.mathnet.ru/eng/msb2807
  • http://mi.mathnet.ru/eng/msb/v145/i2/p253

    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. Sagitov S., “Limit-Theorems for the Multitype Critical Branching-Processes with Immigration”, 271, no. 5, 1983, 1066–1069  mathscinet  zmath  isi
    2. Nakagawa T., “On the Reverse Process of a Critical Multitype Galton-Watson Process Without Variances”, J. Multivar. Anal., 14:1 (1984), 94–100  crossref  mathscinet  zmath  isi
    3. A. L. Yakymiv, “Asymptotic Properties of Subcritical and Supercritical Reduced Branching Processes”, Theory Probab Appl, 30:1 (1986), 201  mathnet  crossref  mathscinet  zmath  isi
    4. Nakagawa T., “Convergence of Critical Multitype Galton-Watson Branching-Processes”, Stoch. Process. Their Appl., 23:2 (1986), 269–279  crossref  mathscinet  zmath  isi
    5. V. A. Vatutin, K. Fleischmann, “Deviations from Typical Type Proportions in Critical Multitype Galton-Watson Processes”, Theory Probab Appl, 45:1 (2001), 23  mathnet  crossref  mathscinet  isi  elib
    6. I. A. Cheltsov, “Regularization of Birational Automorphisms”, Math. Notes, 76:2 (2004), 264–275  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. I. Rahimov, “Limit Theorems for the Size of Subpopulation of Productive Individuals”, Stochastic Models, 20:3 (2004), 261  crossref  mathscinet  zmath
    8. Kevei P., Lopez Mimbela J.A., “Critical Multitype Branching Systems: Extinction Result”, Electron. J. Probab., 16 (2011), 50, 1356–1380  crossref  mathscinet  zmath  isi  elib
    9. Ekaterina Vladimirovna Bulinskaya, “Local Particles Numbers in Critical Branching Random Walk”, J Theor Probab, 2012  crossref  mathscinet
    10. V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with a fixed extinction moment”, Proc. Steklov Inst. Math., 290:1 (2015), 103–124  mathnet  crossref  crossref  isi  elib  elib
    11. V. A. Vatutin, E. E. Dyakonova, V. A. Topchii, “Kriticheskie protsessy Galtona–Vatsona so schetnym mnozhestvom tipov chastits i beskonechnymi vtorymi momentami”, Matem. sb., 212:1 (2021), 3–27  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:313
    Full text:103
    References:55
    First page:2

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