On the continuity and the positivity of the finite part of the limit distribution of an irregular branching process with infinite mean
Keyword(s):
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 = limnU(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.
1980 ◽
Vol 17
(03)
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pp. 696-703
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2017 ◽
Vol 54
(2)
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pp. 569-587
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Keyword(s):
1982 ◽
Vol 19
(03)
◽
pp. 681-684
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Keyword(s):