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Theory of Probability and Mathematical Statistics

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The convergence of Galton-Watson branching processes with immigration to a diffusion process


Author: Ya. M. Khusanbaev
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 179-185
MSC (2000): Primary 60J80; Secondary 60F17, 60J60
DOI: https://doi.org/10.1090/S0094-9000-09-00777-7
Published electronically: December 30, 2009
MathSciNet review: 2494547
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Abstract | References | Similar Articles | Additional Information

Abstract: A sequence of almost critical Galton-Watson branching processes with immigration is studied. Sufficient conditions for the weak convergence of such processes to a diffusion process are found.


References [Enhancements On Off] (What's this?)

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  • 2. T. N. Sriram, Invalidity of bootstrap for critical branching process with immigration, Ann. Statist. 22 (1994), 1013-1023. MR 1292554 (95g:62098)
  • 3. M. Ispany, G. Pap, and M. C. A. Van Zuijlen, Fluctuation limit of branching processes with immigration and estimation of the means, Adv. Appl. Probab. 37 (2005), 523-538.MR 2144565 (2006c:60103)
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Additional Information

Ya. M. Khusanbaev
Affiliation: Department of Probability Theory and Mathematical Statistics, Institute of Mathematics and Information Technologies, F. Khodzhaev Street 29, Tashkent 100125, Uzbekistan
Email: yakubjank@mail.ru

DOI: https://doi.org/10.1090/S0094-9000-09-00777-7
Keywords: Almost critical Galton--Watson branching process with immigration, weak convergence, stochastic differential equation, Skorokhod's space
Received by editor(s): August 6, 2007
Published electronically: December 30, 2009
Article copyright: © Copyright 2009 American Mathematical Society

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