 
Summary: Branching Processes
Population model: each individual has k children (offspring) with
probability pk, independent of all else.
generation 0: ·
generation 1: · ·
generation 2: · · · ·
generation 3: · · · · · · · ·
Applications: population models (family names), nuclear reactions,
club membership, virus on internet, etc.
Let Xn = population size at generation n, then {Xn} is a Markov
chain: branching process.
Let, for i = 1, . . . , Xn,
Z
(n)
i = # children of ith
individual in generation n
and suppose Z
(n)
i are i.i.d. r.v.'s with P(Z = k) = pk
Then X0 = 1 and for n = 0, 1, . . .:
