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This article is cited in 3 scientific papers (total in 3 papers)
On the local limit theorem for critical Galton–Watson process
S. V. Nagaeva, V. I. Vakhtel'b a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Technische Universität München
Abstract:
The proof of the local limit theorem for a critical Galton–Watson process is given under minimal moment restrictions, i.e., under the condition that there exists the second moment of the number of direct offspring of one particle.
Keywords:
Galton–Watson process, Bellman–Harris process, concentration function, local theorem, bilinear generating function.
DOI:
https://doi.org/10.4213/tvp89
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English version:
Theory of Probability and its Applications, 2006, 50:3, 400–419
Bibliographic databases:
Received: 25.04.2003 Revised: 30.01.2004
Citation:
S. V. Nagaev, V. I. Vakhtel', “On the local limit theorem for critical Galton–Watson process”, Teor. Veroyatnost. i Primenen., 50:3 (2005), 457–479; Theory Probab. Appl., 50:3 (2006), 400–419
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/tvp89https://doi.org/10.4213/tvp89 http://mi.mathnet.ru/eng/tvp/v50/i3/p457
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This publication is cited in the following articles:
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Fleischmann K., Wachtel V., “Large deviations for sums indexed by the generations of a Galton–Watson process”, Probability Theory and Related Fields, 141:3–4 (2008), 445–470
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Abraham R., Delmas J.-F., “Local Limits of Conditioned Galton-Watson Trees: the Infinite Spine Case”, Electron. J. Probab., 19 (2014), 2, 1–19
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M. Liu, V. A. Vatutin, “Reduced critical branching processes for small populations”, Theory Probab. Appl., 63:4 (2019), 648–656
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