Conditioned Branching Processes and Their Limiting Diffusions

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Previous article Next article Conditioned Branching Processes and Their Limiting DiffusionsJohn Lamperti and Peter NeyJohn Lamperti and Peter Neyhttps://doi.org/10.1137/1113009PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] William Feller, Diffusion processes in genetics, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 227–246 MR0046022 0045.09302 Google Scholar[2] T. E. Harris, Some mathematical models for branching processes, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 305–328 MR0045331 0045.07701 Google Scholar[3] 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[4] John Lamperti, Limiting distributions for branching processesProc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Vol. II: Contributions to Probability Theory, Part 2, Univ. California Press, Berkeley, Calif., 1967, 225–241 MR0219148 0238.60066 Google Scholar[5] A. M. Yaglom, Certain limit theorems of the theory of branching random processes, Doklady Akad. Nauk SSSR (N.S.), 56 (1947), 795–798 MR0022045 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Hidden symmetries and limit laws in the extreme order statistics of the Laplace random walkThe Annals of Probability, Vol. 50, No. 4 | 1 Jul 2022 Cross Ref Gradient Flow Formulations of Discrete and Continuous Evolutionary Models: A Unifying PerspectiveActa Applicandae Mathematicae, Vol. 171, No. 1 | 5 February 2021 Cross Ref A note on weak convergence results for infinite causal triangulationsBrazilian Journal of Probability and Statistics, Vol. 32, No. 3 | 1 Aug 2018 Cross Ref On branching process with rare neutral mutationBernoulli, Vol. 24, No. 2 | 1 May 2018 Cross Ref Asymptotic Results for Near Critical Bienaymé–Galton–Watson and Catalyst-Reactant Branching ProcessesAdvances in Superprocesses and Nonlinear PDEs | 8 February 2013 Cross Ref Poisson representations of branching Markov and measure-valued branching processesThe Annals of Probability, Vol. 39, No. 3 | 1 May 2011 Cross Ref Continuous-time multitype branching processes conditioned on very late extinctionESAIM: Probability and Statistics, Vol. 15 | 5 January 2012 Cross Ref Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusionsElectronic Journal of Probability, Vol. 13, No. none | 1 Jan 2008 Cross Ref Transformations of Galton-Watson processes and linear fractional reproductionAdvances in Applied Probability, Vol. 39, No. 04 | 1 July 2016 Cross Ref Transformations of Galton-Watson processes and linear fractional reproductionAdvances in Applied Probability, Vol. 39, No. 4 | 1 July 2016 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 Infinite Canonical Super-Brownian Motion and Scaling LimitsCommunications in Mathematical Physics, Vol. 265, No. 3 | 25 May 2006 Cross Ref On a conditional invariance principle for a critical Galton–Watson branching processDiscrete Mathematics and Applications, Vol. 15, No. 1 | 1 Jan 2005 Cross Ref Asymptotic Behaviour of Continuous Time and State Branching ProcessesJournal of the Australian Mathematical Society. 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