Abstract
This paper gives easy proofs of conditional limit laws for the population size Z t of a critical Markov branching process whose offspring law is attracted to a stable law with index 1 + α, where 0 ≤ α ≤ 1. Conditioning events subsume the usual ones, and more general initial laws are considered. The case α = 0 is related to extreme value theory for the Gumbel law.
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