Extinction probability of a branching process
= Extinction probability of a branching process
{title2=$q=\mathbb P(\exists j:Z_j=0)$}
= Branching extinction probability
{synonym}
For a <Galton-Watson process> with one ancestor this is the probability that some generation is empty. It is the smallest fixed point of the offspring <probability generating function> in $[0,1]$; the complementary survival probability is $1-q$. A <branching process conditioned on extinction> reweights reproduction using this fixed point.