Almost sure behavior of linear functionals of supercritical branching processes

Asmussen, Søren

doi:10.1090/S0002-9947-1977-0440719-1

Almost sure behavior of linear functionals of supercritical branching processes
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Trans. Amer. Math. Soc. 231 (1977), 233-248 Request permission

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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