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Analogies between Galton–Watson Processes and $\varphi$-Branching Processes

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Previous article Next article Analogies between Galton–Watson Processes and $\varphi$-Branching ProcessesA. M. ZubkovA. M. Zubkovhttps://doi.org/10.1137/1119036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. A. Sevast'yanov and , A. M. Zubkov, Controlled branching processes, Theory Prob. Applications, 19 (1974), 14–24 10.1137/1119002 0308.60051 LinkGoogle Scholar[2] A. G. Pakes, On the critical Galton-Watson process with immigration, J. Austral. Math. Soc., 12 (1971), 476–482 MR0307370 (46:6490) 0249.60045 CrossrefGoogle Scholar[3] A. M. Zubkov, Life periods of a branching process with immigration, Theory Prob. Application, 17 (1972), 174–183 10.1137/1117018 0267.60084 LinkGoogle Scholar[4] A. G. Pakes, Further results on the critical Galton-Watson process with immigration, J. Austral. Math. Soc., 13 (1972), 277–290 MR0312585 (47:1142) 0235.60078 CrossrefGoogle Scholar[5] B. A. Sevast'yanov, Branching Processes, Izd-vo “Nauka”, Moscow, 1971, (In Russian.) Google Scholar[6] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons Inc., New York, 1966xviii+636 MR0210154 (35:1048) 0138.10207 Google Scholar[7] J. G. Mauldon, On non-dissipative Markov chains, Proc. Cambridge Philos. Soc., 53 (1957), 825–835 MR0092272 (19,1089e) 0088.11102 CrossrefGoogle Scholar[8] Kai Lai Chung, Markov chains with stationary transition probabilities, Die Grundlehren der mathematischen Wissenschaften, Bd. 104, Springer-Verlag, Berlin, 1960x+278 MR0116388 (22:7176) 0092.34304 CrossrefGoogle Scholar[9] H. Kesten and , B. P. Stigum, A limit theorem for multidimensional Galton-Watson processes, Ann. Math. Statist., 37 (1966), 1211–1223 MR0198552 (33:6707) 0203.17401 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Galton--Watson Processes and Their Role as Building Blocks for Branching ProcessesF. Thomas Bruss5 May 2022 | Theory of Probability & Its Applications, Vol. 67, No. 1AbstractPDF (412 KB)Galton-Watson processes and their role as building blocks for branching processes21 January 2022 | Теория вероятностей и ее применения, Vol. 67, No. 1 Cross Ref Bayesian inference for controlled branching processes through MCMC and ABC methodologies24 June 2012 | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, Vol. 107, No. 2 Cross Ref Analysis of a Recurrence Related to Critical Nonhomogeneous Branching ProcessesStochastic Analysis and Applications, Vol. 24, No. 1 Cross Ref Estimation of the variance for a controlled branching processTest, Vol. 14, No. 1 Cross Ref Nonparametric estimation of the offspring distribution and the mean for a controlled branching processTest, Vol. 13, No. 2 Cross Ref On the class of controlled branching processes with random control functions14 July 2016 | Journal of Applied Probability, Vol. 39, No. 4 Cross Ref The age of a Galton-Watson population with a geometric offspring distribution14 July 2016 | Journal of Applied Probability, Vol. 39, No. 4 Cross Ref On the quasi-stationary distribution of a stochastic Ricker modelStochastic Processes and their Applications, Vol. 70, No. 2 Cross Ref A strong law and a central limit theorem for controlled Galton-Watson processes14 July 2016 | Journal of Applied Probability, Vol. 31, No. 1 Cross Ref XVI Seminar on Stability Problems of Stochastic Models17 July 2006 | Theory of Probability & Its Applications, Vol. 37, No. 4AbstractPDF (5240 KB)Mathematische Modelle in der Medizin Cross Ref On recurrence and transience of growth models14 July 2016 | Journal of Applied Probability, Vol. 23, No. 3 Cross Ref On the almost sure convergence of controlled branching processes14 July 2016 | Journal of Applied Probability, Vol. 23, No. 3 Cross Ref A limit theorem for population-size-dependent branching processes14 July 2016 | Journal of Applied Probability, Vol. 22, No. 1 Cross Ref Geometric rate of growth in population-size-dependent branching processes14 July 2016 | Journal of Applied Probability, Vol. 21, No. 1 Cross Ref Lifetimes of Critical Branching Processes with Random MigrationN. M. Yanev and K. V. Mitov17 July 2006 | Theory of Probability & Its Applications, Vol. 28, No. 3AbstractPDF (677 KB)Matrix Functions of Trajectories of Markov ChainsV. P. Chistyakov17 July 2006 | Theory of Probability & Its Applications, Vol. 27, No. 2AbstractPDF (698 KB)Limit Theorems for a Critical Galton–Watson Branching Process with MigrationS. V. Nagaev and L. V. Khan28 July 2006 | Theory of Probability & Its Applications, Vol. 25, No. 3AbstractPDF (683 KB)Positive Recurrence of Multi-Dimensional Population-Dependent Branching Processes Cross Ref A Critical Galton–Watson Branching Process with EmigrationV. A. Vatutin28 July 2006 | Theory of Probability & Its Applications, Vol. 22, No. 3AbstractPDF (941 KB)Conditions for Degeneracy of $\varphi $-Branching Processes with Random $\varphi $N. M. Yanev17 July 2006 | Theory of Probability & Its Applications, Vol. 20, No. 2AbstractPDF (575 KB) Volume 19, Issue 2| 1975Theory of Probability & Its Applications History Submitted:11 December 1973Published online:28 July 2006 InformationCopyright © 1975 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119036Article page range:pp. 309-331ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

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