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Teoriya Veroyatnostei i ee Primeneniya, 1982, Volume 27, Issue 3, Pages 443–455 (Mi tvp2378)  

This article is cited in 13 scientific papers (total in 13 papers)

Transitional phenomena and the convergence of Galton–Watson processes to Jiřina processes

S. A. Alieva, V. M. Šurenkovb

a Baku
b Kiev
Abstract: We show that every transitional phenomenon is connected with a limit theorem describing the convergence of sequences of suitably normalized Galton–Watson processes to the so called continuous state branching processes (introduced by Jiřina).
Received: 24.01.1980
English version:
Theory of Probability and its Applications, 1983, Volume 27, Issue 3, Pages 472–485
DOI: https://doi.org/10.1137/1127057
Bibliographic databases:
Language: Russian
Citation: S. A. Aliev, V. M. Šurenkov, “Transitional phenomena and the convergence of Galton–Watson processes to Jiřina processes”, Teor. Veroyatnost. i Primenen., 27:3 (1982), 443–455; Theory Probab. Appl., 27:3 (1983), 472–485
Citation in format AMSBIB
\Bibitem{AliShu82}
\by S.~A.~Aliev, V.~M.~{\v S}urenkov
\paper Transitional phenomena and the convergence of Galton--Watson processes to Jiřina processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1982
\vol 27
\issue 3
\pages 443--455
\mathnet{http://mi.mathnet.ru/tvp2378}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=673918}
\zmath{https://zbmath.org/?q=an:0565.60068}
\transl
\jour Theory Probab. Appl.
\yr 1983
\vol 27
\issue 3
\pages 472--485
\crossref{https://doi.org/10.1137/1127057}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1983RJ51700004}
Linking options:
  • https://www.mathnet.ru/eng/tvp2378
  • https://www.mathnet.ru/eng/tvp/v27/i3/p443
  • This publication is cited in the following 13 articles:
    1. Rongjuan Fang, Zenghu Li, Jiawei Liu, “A Scaling Limit Theorem for Galton–Watson Processes in Varying Environments”, Proc. Steklov Inst. Math., 316 (2022), 137–159  mathnet  crossref  crossref
    2. Rongjuan Fang, Zenghu Li, “Construction of continuous-state branching processes in varying environments”, Ann. Appl. Probab., 32:5 (2022)  crossref
    3. Limnios N., Yarovaya E., “Diffusion Approximation of Branching Processes in Semi-Markov Environment”, Methodol. Comput. Appl. Probab., 22:4 (2020), 1583–1590  crossref  isi
    4. Zenghu Li, Mathematical Lectures from Peking University, From Probability to Finance, 2020, 1  crossref
    5. Limnios N., Yarovaya E., “Diffusion Approximation of Near Critical Branching Processes in Fixed and Random Environment”, Stoch. Models, 35:2 (2019), 209–220  crossref  mathscinet  isi  scopus
    6. Zenghu Li, “Sample paths of continuous-state branching processes with dependent immigration”, Stochastic Models, 35:2 (2019), 167  crossref
    7. D. V. Pilshchikov, “On the limiting mean values in probabilistic models of time-memory-data tradeoff methods”, Matem. vopr. kriptogr., 6:2 (2015), 59–65  mathnet  crossref  mathscinet  elib
    8. D. V. Pilshchikov, “Estimation of the characteristics of time-memory-data tradeoff methods via generating functions of the number of particles and the total number of particles in the Galton–Watson process”, Matem. vopr. kriptogr., 5:2 (2014), 103–108  mathnet  crossref
    9. Hongwei Bi, “Time to most recent common ancestor for stationary continuous state branching processes with immigration”, Front. Math. China, 9:2 (2014), 239  crossref
    10. Pakes A.G., “A limit theorem for the maxima of the para–critical simple branching process”, Advances in Applied Probability, 30:3 (1998), 740–756  crossref  mathscinet  zmath  isi
    11. S. M. Sagitov, “A multidimensional critical branching process generated by a large number of particles of a single type”, Theory Probab. Appl., 35:1 (1991), 118–130  mathnet  mathnet  crossref  isi
    12. K. A. Borovkov, “A Method of Proof of Limit Theorems for Branching Processes”, Theory Probab. Appl., 33:1 (1988), 105–113  mathnet  mathnet  crossref  isi
    13. K. A. Borovkov, “On the rate of convergence of branching processes to a diffusion one”, Theory Probab. Appl., 30:3 (1986), 496–506  mathnet  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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