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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Almost sure behavior of linear functionals of supercritical branching processes


Author: Søren Asmussen
Journal: Trans. Amer. Math. Soc. 231 (1977), 233-248
MSC: Primary 60J80
DOI: https://doi.org/10.1090/S0002-9947-1977-0440719-1
MathSciNet review: 0440719
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Abstract: The exact a.s. behavior of any linear functional $ {Z_n} \cdot a$ of a supercritical positively regular p-type $ (1 < p < \infty )$ Galton-Watson process $ \{ {Z_n}\} $ is found under a second moment hypothesis. The main new results are of iterated logarithm type, with normalizing constants depending on the decomposition of a according to the Jordan canonical form of the offspring mean matrix.


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DOI: https://doi.org/10.1090/S0002-9947-1977-0440719-1
Keywords: Galton-Watson process, multitype, supercritical, linear functional, Jordan canonical form, law of the iterated logarithm
Article copyright: © Copyright 1977 American Mathematical Society

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