A Refinement of Two Theorems in the Theory of Branching Processes

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Previous article Next article A Refinement of Two Theorems in the Theory of Branching ProcessesC. R. Heathcote, E. Seneta, and D. Vere-JonesC. R. Heathcote, E. Seneta, and D. Vere-Joneshttps://doi.org/10.1137/1112033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Theodore E. Harris, The theory of branching processes, Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin, 1963xiv+230 MR0163361 0117.13002 CrossrefGoogle Scholar[2] A. N. Kolmogorov, On a solution of a biological problem, Izv. NII Matem. Mekh. Tomskogo Univ., 2 (1938), 7–12, (In Russian.) Google Scholar[3] Hellmuth Kneser, Reelle analytische Lösungen der Gleichung $\varphi(\varphi(x))=e\sp x$ und verwandter Funktional-gleichungen, J. Reine Angew. Math., 187 (1949), 56–67 MR0035385 0035.04801 Google Scholar[4] Marek Kuczma, Sur une équation fonctionnelle, Mathematica (Cluj), 3 (26) (1961), 79–87 MR0150495 0104.09502 Google Scholar[5] Marek Kuczma, Note on Schröder's functional equation, J. Austral. Math. Soc., 4 (1964), 149–151 MR0165266 0163.38502 CrossrefGoogle Scholar[6] A. V. Nagaev, Sharpening of several theorems in the theory of branching processes, Trudy Tashkentogo Univ., 189 (1961), 55–63, (In Russian.) Google Scholar[7] A. M. Yaglom, Certain limit theorems of the theory of branching random processes, Doklady Akad. Nauk SSSR (N.S.), 56 (1947), 795–798, (In Russian.) MR0022045 Google Scholar[8] V. M. Zolotarev, More exact statements of several theorems in the theory of branching processes, Theory Prob. Applications, 2 (1957), 245–253, (English translation.) 10.1137/1102016 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Quasi-stationary distributions for subcritical superprocessesStochastic Processes and their Applications, Vol. 132 | 1 Feb 2021 Cross Ref A Low-Rank Technique for Computing the Quasi-Stationary Distribution of Subcritical Galton--Watson ProcessesSophie Hautphenne and Stefano MasseiSIAM Journal on Matrix Analysis and Applications, Vol. 41, No. 1 | 9 January 2020AbstractPDF (1587 KB)On the maximal offspring in a subcritical branching processElectronic Journal of Probability, Vol. 25, No. none | 1 Jan 2020 Cross Ref The $\lambda$-invariant measures of subcritical Bienaymé–Galton–Watson processesBernoulli, Vol. 24, No. 1 | 1 Feb 2018 Cross Ref Limit theorems for conditioned non-generic Galton–Watson treesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 51, No. 2 | 1 May 2015 Cross Ref Biased random walks on Galton–Watson trees with leavesThe Annals of Probability, Vol. 40, No. 1 | 1 Jan 2012 Cross Ref Quasi-Stationary Distributions and the Continuous-State Branching Process Conditioned to Be Never ExtinctElectronic Journal of Probability, Vol. 12, No. none | 1 Jan 2007 Cross Ref The age of a Galton-Watson population with a geometric offspring distributionJournal of Applied Probability, Vol. 39, No. 04 | 14 July 2016 Cross Ref The age of a Galton-Watson population with a geometric offspring distributionJournal of Applied Probability, Vol. 39, No. 4 | 14 July 2016 Cross Ref Elementary new proofs of classical limit theorems for Galton–Watson processesJournal of Applied Probability, Vol. 36, No. 02 | 14 July 2016 Cross Ref Elementary new proofs of classical limit theorems for Galton–Watson processesJournal of Applied Probability, Vol. 36, No. 2 | 14 July 2016 Cross Ref Branching Processes and Their Applications in the Analysis of Tree Structures and Tree AlgorithmsProbabilistic Methods for Algorithmic Discrete Mathematics | 1 Jan 1998 Cross Ref Extinction Probabilities for Branching Processes Bounded from BelowB. 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