The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation.

Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.

Miguel González Velasco is Associate Professor at the University of Extremadura in Spain. His research interests lie in the theory of branching processes and its application to genetics, epidemiology and population dynamics.

Inés M. del Puerto García is Associate Professor at the University of Extremadura in Spain. Her research interests include the study of the probabilistic and inferential theory on branching processes.

George P. Yanev is Associate Professor at the University of Texas Rio Grande Valley in the USA. His research interests include branching processes and characterizations of probability distributions.