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Branching Processes Population model: each individual has k children (offspring) with
 

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, . . .:

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering