Abstract
It is shown that the limiting random variable W(si
) of an irregular branching process with infinite mean, defined in [5], has a continuous and positive distribution on {0 < W(si
) < ∞}. This implies that for all branching processes (Zn
) with infinite mean there exists a function U such that the distribution of V = lim
n
U(Zn
)e–n
a.s. is continuous, positive and finite on the set of non-extinction. A kind of law of large numbers for sequences of independent copies of W(si
) is derived.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
4 articles.
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