Seminario Estadística UAM
Carmen Minuesa Abril, Universidad de Extremadura
"Branching processes with applications in Biology"
Aula 520, Módulo 17, Facultad de Ciencias, Universidad Autónoma de Madrid
Martes 21 de mayo de 2019
Resumen: Branching processes are stochastic models applied in the development of theoretical approaches to problems in fields such as growth and extinction of populations, biology, epidemiology, cell proliferation, kinetics, genetics and algorithm and data structures. The most basic model, known as the Bienaymé-Galton-Watson process or simply the Galton-Watson process, consists in individuals that have offspring independently of the others and following the same probability distribution. However, this model was inappropriate to tackle some complex problems that had arisen in different fields of knowledge. This fact has motivated the introduction of new branching processes, both in discrete and continuous time. In this talk, we explore some limitations of the Galton-Watson process in different biological contexts and present some discrete-time branching processes that generalise the previous model, such as the controlled branching process, the branching process in a varying environment, the defective branching process or the population-size-dependent branching process.