El procés de ramificació de Galton-Watson: el problema de l'extinció dels cognoms

Abstract

From ancient times, people have been worried about the possibility of their lineages and surnames being extinguished. This question affected, above all, to the highest classes. Even though they looked for social and/or biological conditions at the beginning, the problem was focused from a statistic perspective during the 18th and 19th centuries. The main objective of our work is studying the mathematical model behind this question, known as the branching process of Galton-Watson. Once the main results of this theory have been developed, we will be able to calculate the extinction probability of a population or family, though also we will be able to estimate it from a set of empirical observations.