Il processo di Galton-Watson: teoria e simulazione

A Galton-Watson process is a integer valued Markov chain. Its transition function can be defined through the distribution of a random variable called "offspring". It can be classified as supercritical if the mean of such random variable is greater than 1. The generating function of a supercritical Galton-Watson process can be transformed to obtain the generating function of a process that describes the "backbone" of the original tree, where the "backbone" is the branching containing all the particles that present an infinite line of descendants. With the use of a particular order of the particles, I was able to entirely describe any tree by a string. Such string can be used to obtain sub-branches and their trajectories. Using C++, I implemented this algorithm and I used it to obtain the "empiric backbone" of a tree generated as a Galton-Watson process. Then I showed the condition under which the "empiric backbone" is a good approximation of the "backbone".