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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Almost sure behavior of linear functionals of supercritical branching processes
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by Søren Asmussen
Trans. Amer. Math. Soc. 231 (1977), 233-248
DOI: https://doi.org/10.1090/S0002-9947-1977-0440719-1

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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Bibliographic Information
  • © Copyright 1977 American Mathematical Society
  • 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