The Asymptotic Probability of the First Degeneration for Branching Processes with Immigration

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Previous article Next article The Asymptotic Probability of the First Degeneration for Branching Processes with ImmigrationV. A. VatutinV. A. Vatutinhttps://doi.org/10.1137/1119003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] T. E. Harris, Theory of Branching Processes, Prentice-Hail, Inc., Englewood Cliffs, N.J., 1964 0117.13002 Google Scholar[2] A. M. Zubkov, Life-periods of a branching process with immigration, Theory Prob. Applications, 17 (1972), 174–183 10.1137/1117018 0267.60084 LinkGoogle Scholar[3] B. A. Sevast'yanov, Branching Processes, Izd-vo Nauka, Moscow, 1971, (In Russian.) Google Scholar[4A] William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons Inc., New York, 1968xviii+509 MR0228020 (37:3604) 0155.23101 Google Scholar[4B] William Feller, An introduction to probability theory and its applications. Vol. II, Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 MR0270403 (42:5292) 0219.60003 Google Scholar[5] V. M. Zolotarev, More exact statements of several theorems in the theory of branching processes, Theory Prob. Applications, 2 (1957), 245–253 10.1137/1102016 LinkGoogle Scholar[6] H. Kesten, , P. Ney and , F. Spitzer, The Galton-Watson branching process with mean one and finite variance, Theory Prob. Applications, 11 (1966), 513–540 10.1137/1111059 0158.35202 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The Tail of the Length of an Excursion in a Trap of Random Size6 July 2022 | Journal of Statistical Physics, Vol. 188, No. 3 Cross Ref The down/up crossing properties of weighted Markov branching processes20 January 2021 | SCIENTIA SINICA Mathematica, Vol. 52, No. 4 Cross Ref Long time behaviour for Markovian branching-immigration systems2 July 2020 | Discrete Event Dynamic Systems, Vol. 31, No. 1 Cross Ref Regularity criterion for 2-type Markov branching processes with immigrationStatistics & Probability Letters, Vol. 121 Cross Ref Markov branching processes with killing and resurrection1 October 2015 | Science China Mathematics, Vol. 59, No. 3 Cross Ref Asymptotic Properties of the Markov Branching Process with Immigration27 July 2010 | Journal of Theoretical Probability, Vol. 25, No. 1 Cross Ref Time to Extinction of Galton–Watson Processes Censored at High LevelV. A. Topchii21 May 2010 | Theory of Probability & Its Applications, Vol. 54, No. 2AbstractPDF (231 KB)Existence, uniqueness and ergodicity of Markov branching processes with immigration and instantaneous resurrection7 May 2008 | Science in China Series A: Mathematics, Vol. 51, No. 7 Cross Ref Ch. 18. Biological applications of branching processes Cross Ref Volume 19, Issue 1| 1974Theory of Probability & Its Applications History Submitted:29 October 1973Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119003Article page range:pp. 25-34ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics