|
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
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:
-
Sagitov S., “Limit-Theorems for the Multitype Critical Branching-Processes with Immigration”, 271, no. 5, 1983, 1066–1069
-
Nakagawa T., “On the Reverse Process of a Critical Multitype Galton-Watson Process Without Variances”, J. Multivar. Anal., 14:1 (1984), 94–100
-
A. L. Yakymiv, “Asymptotic Properties of Subcritical and Supercritical Reduced Branching Processes”, Theory Probab Appl, 30:1 (1986), 201
 -
Nakagawa T., “Convergence of Critical Multitype Galton-Watson Branching-Processes”, Stoch. Process. Their Appl., 23:2 (1986), 269–279
-
V. A. Vatutin, K. Fleischmann, “Deviations from Typical Type Proportions in Critical Multitype Galton-Watson Processes”, Theory Probab Appl, 45:1 (2001), 23
 -
I. A. Cheltsov, “Regularization of Birational Automorphisms”, Math. Notes, 76:2 (2004), 264–275
-
I. Rahimov, “Limit Theorems for the Size of Subpopulation of Productive Individuals”, Stochastic Models, 20:3 (2004), 261
-
Kevei P., Lopez Mimbela J.A., “Critical Multitype Branching Systems: Extinction Result”, Electron. J. Probab., 16 (2011), 50, 1356–1380
-
Ekaterina Vladimirovna Bulinskaya, “Local Particles Numbers in Critical Branching Random Walk”, J Theor Probab, 2012
-
V. A. Vatutin, E. E. D'yakonova, “Decomposable branching processes with a fixed extinction moment”, Proc. Steklov Inst. Math., 290:1 (2015), 103–124
-
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
|
| Number of views: |
| This page: | 313 | | Full text: | 103 | | References: | 55 | | First page: | 2 |
|
Terms of Use