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On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random Environment

1977; Society for Industrial and Applied Mathematics; Volume: 21; Issue: 4 Linguagem: Inglês

10.1137/1121091

ISSN

1095-7219

Autores

M. V. Kozlov,

Tópico(s)

Probability and Risk Models

Resumo

Previous article Next article On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random EnvironmentM. V. KozlovM. V. Kozlovhttps://doi.org/10.1137/1121091PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Walter L. Smith and , William E. Wilkinson, On branching processes in random environments, Ann. Math. Statist., 40 (1969), 814–827, no. 3 MR0246380 0184.21103 CrossrefGoogle Scholar[2A] Krishna B. Athreya and , Samuel Karlin, On branching processes with random environments. I. Extinction probabilities, Ann. Math. Statist., 42 (1971), 1499–1520 MR0298780 0228.60032 CrossrefGoogle Scholar[2B] Krishna B. Athreya and , Samuel Karlin, Branching processes with random environments. II. Limit theorems, Ann. Math. Statist., 42 (1971), 1843–1858 MR0298781 0228.60033 CrossrefGoogle Scholar[3] A. N. Kolmogorov, On the solution of a biological problem, Izv. Nil. Matem. i Meh. Tomskogo Un-ta., 2 (1938), 7–12, (In Russian.) Google Scholar[4] H. Kesten, , M. V. Kozlov and , F. Spitzer, A limit law for random walk in a random environment, Compositio Math., 30 (1975), 145–168 MR0380998 0388.60069 Google Scholar[5] Alan Agresti, Bounds on the extinction time distribution of a branching process, Advances in Appl. Probability, 6 (1974), 322–335 MR0423562 0293.60077 CrossrefGoogle Scholar[6] Alan Agresti, On the extinction times of varying and random environment branching processes, J. Appl. Probability, 12 (1975), 39–46 MR0365733 0306.60052 CrossrefGoogle Scholar[7] William Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 MR0270403 0219.60003 Google Scholar[8] Donald L. Iglehart, Functional central limit theorems for random walks conditioned to stay positive, Ann. Probability, 2 (1974), 608–619 MR0362499 0299.60053 CrossrefGoogle Scholar[9] D. J. Emery, Limiting behaviour of the distributions of the maxima of partial sums of certain random walks, J. Appl. Probability, 9 (1972), 572–579 MR0345200 0242.60027 CrossrefGoogle Scholar[10] N. H. Bingham, Limit theorems in fluctuation theory, Advances in Appl. Probability, 5 (1973), 554–569 MR0348843 0273.60066 CrossrefGoogle Scholar[11] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949xvi+396 MR0030620 0032.05801 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Limit theorems for critical branching processes in a finite-state-space Markovian environmentAdvances in Applied Probability, Vol. 8 | 1 March 2022 Cross Ref Условная $L^1$-сходимость для мартингала критического ветвящегося процесса в случайной средеТруды Математического института имени В. А. Стеклова, Vol. 316 | 19 April 2022 Cross Ref Большие уклонения строго докритического ветвящегося процесса в случайной средеТруды Математического института имени В. А. 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