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).
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
\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:
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
Rongjuan Fang, Zenghu Li, “Construction of continuous-state branching processes in varying environments”, Ann. Appl. Probab., 32:5 (2022)
Limnios N., Yarovaya E., “Diffusion Approximation of Branching Processes in Semi-Markov Environment”, Methodol. Comput. Appl. Probab., 22:4 (2020), 1583–1590
Zenghu Li, Mathematical Lectures from Peking University, From Probability to Finance, 2020, 1
Limnios N., Yarovaya E., “Diffusion Approximation of Near Critical Branching Processes in Fixed and Random Environment”, Stoch. Models, 35:2 (2019), 209–220
Zenghu Li, “Sample paths of continuous-state branching processes with dependent immigration”, Stochastic Models, 35:2 (2019), 167
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
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
Hongwei Bi, “Time to most recent common ancestor for stationary continuous state branching processes with immigration”, Front. Math. China, 9:2 (2014), 239
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
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
K. A. Borovkov, “A Method of Proof of Limit Theorems for Branching Processes”, Theory Probab. Appl., 33:1 (1988), 105–113
K. A. Borovkov, “On the rate of convergence of branching processes to a diffusion one”, Theory Probab. Appl., 30:3 (1986), 496–506