Galton–Watson Process Attaining a High Level

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Previous article Next article Galton–Watson Process Attaining a High LevelV. I. AfanasyevV. I. Afanasyevhttps://doi.org/10.1137/S0040585X97983183PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractLimit theorems are established for a critical Galton–Watson process attaining a high level describing the distributions of the time to attain this level and the life length of the process.[1] T. Lindvall, On the maximum of a branching process, Scand. J. Statist., 3 (1976), pp. 209–214. SJSADG 0303-6898 Google Scholar[2] K. A. Borovkov and and V. A. Vatutin, On distribution tails and expectations of maxima in critical branching processes, J. Appl. Probab., 33 (1996), pp. 614–622. JPRBAM 0021-9002 CrossrefGoogle Scholar[3] R. T. Durrett, Conditioned limit theorems for some null recurrent Markov processes, Ann. Probab., 6 (1978), pp. 798–828. APBYAE 0091-1798 CrossrefGoogle Scholar[4] T. Lindvall, Convergence of critical Galton–Watson branching processes, J. Appl. Probab., 9 (1972), pp. 445–450. JPRBAM 0021-9002 CrossrefGoogle Scholar[5] T. Lindvall, Limit theorems for some functionals of certain Galton–Watson branching processes, Adv. Appl. Probab., 6 (1974), pp. 309–321. AAPBBD 0001-8678 CrossrefGoogle Scholar[6] A. G. Pakes, A limit theorem for the maxima of the para-critical simple branching process, Adv. Appl. Probab., 30 (1998), pp. 740–756. AAPBBD 0001-8678 CrossrefGoogle Scholar[7] Google ScholarKeywordsGalton–Watson processtime to attain a levellife lengthconditional invariance principlesconditional limit theoremsmodified Bessel functions Previous article Next article FiguresRelatedReferencesCited byDetails On the Local Time of a Stopped Random Walk Attaining a High Level27 April 2022 | Proceedings of the Steklov Institute of Mathematics, Vol. 316, No. 1 Cross Ref О локальном времени остановленного случайного блуждания, достигающего высокого уровня19 April 2022 | Труды Математического института имени В. А. Стеклова, Vol. 316 Cross Ref The Analysis of Factors and Motivative Aspects Promoting and Hindering the Implementation of Precision Farming Technologies16 December 2020 | WSEAS TRANSACTIONS ON ENVIRONMENT AND DEVELOPMENT, Vol. 16 Cross Ref Invariance Principle for a Critical Galton–Watson Process Attaining a High LevelV. I. Afanasyev10 November 2011 | Theory of Probability & Its Applications, Vol. 55, No. 4AbstractPDF (183 KB) Volume 52, Issue 3| 2008Theory of Probability & Its Applications History Submitted:29 March 2005Published online:27 August 2008 InformationCopyright © 2008 Society for Industrial and Applied MathematicsKeywordsGalton–Watson processtime to attain a levellife lengthconditional invariance principlesconditional limit theoremsmodified Bessel functionsPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97983183Article page range:pp. 509-515ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics