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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Some limit theorems for controlled branching processes


Author: Ya. M. Khusanbaev
Translated by: O. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 51-58
MSC (2000): Primary 60J80; Secondary 60F17, 60J65
Published electronically: January 18, 2011
MathSciNet review: 2667309
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Abstract: Limit theorems are obtained for branching processes depending on the size of the population. These results contain the case of convergence of such processes to the deterministic limit. Functional central limit theorems for fluctuations are proved.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0094-9000-2010-00809-X
Keywords: Population-size-dependent branching process, weak convergence, Wiener process, limit theorem
Received by editor(s): August 6, 2007
Published electronically: January 18, 2011
Article copyright: © Copyright 2010 American Mathematical Society



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