A Class of Limit Theorems for a Critical Bellman–Harris Branching Process

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Previous article Next article A Class of Limit Theorems for a Critical Bellman–Harris Branching ProcessV. A. VatutinV. A. Vatutinhttps://doi.org/10.1137/1126087PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. A. Vatutin, Limit theorems for a critical Bellman-Harris branching process with infinite variance, Theory Prob. Appl., 21 (1976), 839–842 0383.60079 LinkGoogle Scholar[2] V. A. Vatutin, Discrete limit distributions of the particle number in critical Bellman-Harris branching processes, Theory Prob. Appl., 22 (1977), 146–152 0391.60082 LinkGoogle Scholar[3] V. A. Vatutin, A new limit theorem for a critical Bellman-Harris branching process, Mat. Sb. (N.S.), 109(151) (1979), 440–452, 480 81b:60085 0443.60080 Google Scholar[4] S. V. Nagaev, Transition phenomena for age-dependent branching processes with discrete time. II, Sibirsk. Mat. Ž., 15 (1974), 570–579, 701 50:14975 0294.60065 Google Scholar[5] W. Feller, An Introduction to the Theory of Probability and Its Applications, Vol. II, John Wiley, New York, 1966 Google Scholar[6] T. Harris, The theory of branching processes, Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin, 1963xiv+230 29:664 0117.13002 CrossrefGoogle Scholar[7] B. V. Shabat, Introduction to Complex Analysis, Part 1, Nauka, Moscow, 1976, (In Russian.) Google Scholar[8] Martin I. Goldstein, Critical age-dependent branching processes: Single and multitype, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 17 (1971), 74–88 43:4132 0212.19704 CrossrefGoogle Scholar[9] Martin I. Goldstein and , Fred M. Hoppe, Limit theorems for the critical age-dependent branching process with infinite variance, Stochastic Processes Appl., 5 (1977), 297–305 10.1016/0304-4149(77)90037-0 56:16811 0369.60101 CrossrefGoogle Scholar[10] Eugene Seneta, Regularly varying functions, Springer-Verlag, Berlin, 1976, 88– 56:12189 CrossrefGoogle Scholar[11] R. S. Slack, A branching process with mean one and possibly infinite variance, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 9 (1968), 139–145 37:3661 0164.47002 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Decomposable Critical Bellman–Harris Branching Process with Two Particle Types. IIV. A. Vatutin and S. M. SagitovTheory of Probability & Its Applications, Vol. 34, No. 2 | 17 July 2006AbstractPDF (790 KB) Volume 26, Issue 4| 1982Theory of Probability & Its Applications657-870 History Submitted:27 March 1980Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1126087Article page range:pp. 806-812ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics