A stochastic process with varying numbers of states. Consider a population in which each individual has probability pk of providing k descendants in the next generation. Let Xj be the number of individuals in the jth generation. The sequence X1, X2,…, is a Markov process known as a branching process. This formulation was originally suggested by Galton and Henry Watson in 1874 in the context of the extinction of surnames, and may be referred to as the Galton–Watson model. Extinction is certain if and only if and otherwise the probability of extinction is equal to P, the solution (between 0 and 1) of .
Subjects: Probability and Statistics.