Abstract

Previous article Next article The Galton-Watson Process with Mean One and Finite VarianceH. Kesten, P. Ney, and F. SpitzerH. Kesten, P. Ney, and F. Spitzerhttps://doi.org/10.1137/1111059PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. P. Chistyakov, Local limit theorems in the theory of branching random processes, Theory Prob. Applications, 2 (1957), 345–363, (English translation.) 10.1137/1102024 LinkGoogle Scholar[2] Howard Conner, A note on limit theorems for Markov branching processes, Proc. Amer. Math. Soc., 18 (1967), 76–86 MR0203819 0147.16305 CrossrefGoogle Scholar[3] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[4] J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech., 8 (1959), 433–458; erratum 993 MR0107098 0101.11503 Google Scholar[5] G. H. Hardy and , J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet's series whose coefficients are positive, Proc. London Math. Soc., Ser. 2, 13 (1914), 171–191 Google Scholar[6] 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[7] Samuel Karlin and , James McGregor, Uniqueness of stationary measures for branching processes and applicationsProc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), Univ. California Press, Berkeley, Calif., 1967, Vol. II: Contributions to Probability Theory, Part 2, pp. 243–254 MR0214154 0218.60074 Google Scholar[8] J. F. G. Kingman, Stationary measures for branching processes, Proc. Amer. Math. Soc., 16 (1965), 245–247 MR0173291 0132.38305 CrossrefGoogle Scholar[9] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953x+190 MR0054173 0052.11701 Google Scholar[10] Jacques Neveu, Chaı⁁nes de Markov et théorie du potentiel, Ann. Fac. Sci. Univ. Clermont-Ferrand, (1964), 37–89, (Math) MR0386031 Google Scholar[11] B. A. Rogozin, An estimate for concentration functions, Theory Prob. Applications, 6 (1961), 94–97, (English translation.) 10.1137/1106009 0106.34002 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails О генеалогической структуре критических ветвящихся процессов в меняющейся среде19 April 2022 | Труды Математического института имени В. А. Стеклова, Vol. 316 Cross Ref On the Genealogical Structure of Critical Branching Processes in a Varying Environment27 April 2022 | Proceedings of the Steklov Institute of Mathematics, Vol. 316, No. 1 Cross Ref Harmonic moments and large deviations for a critical Galton-Watson process with immigration7 April 2021 | Science China Mathematics, Vol. 64, No. 8 Cross Ref The Horton–Strahler number of conditioned Galton–Watson treesElectronic Journal of Probability, Vol. 26, No. none Cross Ref Bienaymé–Galton–Watson Simple Branching Process and Extinction9 June 2021 Cross Ref Unimodular Hausdorff and Minkowski dimensionsElectronic Journal of Probability, Vol. 26, No. none Cross Ref Penalization of Galton–Watson processesStochastic Processes and their Applications, Vol. 130, No. 5 Cross Ref Critical percolation and the incipient infinite cluster on Galton-Watson treesElectronic Communications in Probability, Vol. 24, No. none Cross Ref Speeding up non-Markovian first-passage percolation with a few extra edges16 November 2018 | Advances in Applied Probability, Vol. 50, No. 3 Cross Ref Large deviation principle for the maximal positions in critical branching random walks with small driftsStatistics & Probability Letters, Vol. 139 Cross Ref A 2-spine decomposition of the critical Galton-Watson tree and a probabilistic proof of Yaglom’s theoremElectronic Communications in Probability, Vol. 23, No. none Cross Ref The dimension of the range of a transient random walkElectronic Journal of Probability, Vol. 23, No. none Cross Ref Limit theorems for some critical superprocessesIllinois Journal of Mathematics, Vol. 59, No. 1 Cross Ref Critical random graphs: Diameter and mixing timeThe Annals of Probability, Vol. 36, No. 4 Cross Ref Quasi-Stationary Regime of a Branching Random Walk in Presence of an Absorbing Wall4 March 2008 | Journal of Statistical Physics, Vol. 131, No. 2 Cross Ref Small-time behavior of beta coalescentsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 44, No. 2 Cross Ref Mixing Time Power Laws at Criticality Cross Ref On the Local Limit Theorem for a Critical Galton–Watson ProcessS. V. Nagaev and V. I. Vakhtel15 August 2006 | Theory of Probability & Its Applications, Vol. 50, No. 3AbstractPDF (190 KB)Limit theorems for probabilities of large deviations of a Galton–Watson processDiscrete Mathematics and Applications, Vol. 13, No. 1 Cross Ref The Survival Probability of a Critical Branching Process in a Random EnvironmentJ. Geiger and G. Kersting25 July 2006 | Theory of Probability & Its Applications, Vol. 45, No. 3AbstractPDF (152 KB)Growth rates of sample covariances of stationary symmetric α-stable processes associated with null recurrent Markov chainsStochastic Processes and their Applications, Vol. 85, No. 2 Cross Ref Asymptotic Behaviour of Continuous Time and State Branching Processes9 April 2009 | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 68, No. 1 Cross Ref A new proof of Yaglom’s exponential limit law Cross Ref Processus de Branchement, Arbres et Superprocessus Cross Ref Elementary new proofs of classical limit theorems for Galton–Watson processes14 July 2016 | Journal of Applied Probability, Vol. 36, No. 02 Cross Ref Elementary new proofs of classical limit theorems for Galton–Watson processes14 July 2016 | Journal of Applied Probability, Vol. 36, No. 2 Cross Ref Branching Processes and Their Applications in the Analysis of Tree Structures and Tree Algorithms Cross Ref Sharpness of Second Moment Criteria for Branching and Tree-Indexed Processes Cross Ref Limit Theorems for the Total Number of Descendants for the Galton–Watson Branching ProcessA. V. Karpenko and S. V. Nagaev17 July 2006 | Theory of Probability & Its Applications, Vol. 38, No. 3AbstractPDF (1902 KB)Some asymptotic results for the branching process with immigrationStochastic Processes and their Applications, Vol. 31, No. 2 Cross Ref Local Limit Theorems for Critical Galton–Watson Processes with Decreasing ImmigrationI. Rakhimov17 July 2006 | Theory of Probability & Its Applications, Vol. 33, No. 2AbstractPDF (454 KB)Green function behaviour of critical Galton-Watson processes with immigrationBoletim da Sociedade Brasileira de Matemática, Vol. 14, No. 1 Cross Ref Comments on the age distribution of Markov processes1 July 2016 | Advances in Applied Probability, Vol. 13, No. 04 Cross Ref Comments on the age distribution of Markov processes1 July 2016 | Advances in Applied Probability, Vol. 13, No. 4 Cross Ref Estimacion de la edad y del numero inicial de individuos en procesos de nacimiento puro y de Galton-WatsonTrabajos de estadistica y de investigacion operativa, Vol. 32, No. 1 Cross Ref On the stationary measures of critical branching processesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 55, No. 3 Cross Ref Effective population numbers and mean times to extinction in monoecious populations with overlapping generationsMathematical Biosciences, Vol. 46, No. 1-2 Cross Ref The genealogy of critical branching processesStochastic Processes and their Applications, Vol. 8, No. 1 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)A local limit theorem for the critical age-dependent branching process14 July 2016 | Journal of Applied Probability, Vol. 15, No. 01 Cross Ref A local limit theorem for the critical age-dependent branching process14 July 2016 | Journal of Applied Probability, Vol. 15, No. 1 Cross Ref Probability of extinction of critical generation-dependent Galton–Watson processes14 July 2016 | Journal of Applied Probability, Vol. 13, No. 03 Cross Ref Probability of extinction of critical generation-dependent Galton–Watson processes14 July 2016 | Journal of Applied Probability, Vol. 13, No. 3 Cross Ref A generalization of Goldstein's comparison lemma and the exponential limit law in critical Crump-Mode-Jagers branching processes1 July 2016 | Advances in Applied Probability, Vol. 8, No. 01 Cross Ref A generalization of Goldstein's comparison lemma and the exponential limit law in critical Crump-Mode-Jagers branching processes1 July 2016 | Advances in Applied Probability, Vol. 8, No. 1 Cross Ref The Asymptotic Probability of the First Degeneration for Branching Processes with ImmigrationV. A. Vatutin28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 1AbstractPDF (613 KB)Extinction probability for a critical general branching processStochastic Processes and their Applications, Vol. 2, No. 3 Cross Ref Limit theorems for some functionals of certain Galton-Watson branching processes1 July 2016 | Advances in Applied Probability, Vol. 6, No. 2 Cross Ref Processus de Galton-Watson6 September 2006 Cross Ref Life-Periods of a Branching Process with ImmigrationA. M. Zubkov17 July 2006 | Theory of Probability & Its Applications, Vol. 17, No. 1AbstractPDF (695 KB)Critical age-dependent branching processes: Single and multitypeZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 17, No. 1 Cross Ref Heavy traffic approximations for the Galton-Watson process1 July 2016 | Advances in Applied Probability, Vol. 3, No. 02 Cross Ref Heavy traffic approximations for the Galton-Watson process1 July 2016 | Advances in Applied Probability, Vol. 3, No. 2 Cross Ref On the spectral representation of branching processes with mean oneJournal of Mathematical Analysis and Applications, Vol. 21, No. 3 Cross Ref Volume 11, Issue 4| 1966Theory of Probability & Its Applications History Submitted:23 May 1966Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1111059Article page range:pp. 513-540ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call