Title: Weak convergence results in the class of controlled branching processes
Authors: Pedro Martin-Chavez - University of Extremadura (Spain) [presenting]
Miguel Gonzalez Velasco - University of Extremadura (Spain)
Ines M del Puerto - University of Extremadura (Spain)
Abstract: The study of functional weak limit theorems for branching processes aroused a lot of interest since 1951, when the convergence of standard Bienayme Galton Watson processes (BGWPs), suitably scaled, to a class of diffusion processes, was established. The aim is to contribute, focusing the attention on a more general class of branching processes. Concretely, we consider controlled branching processes. It is a wide family of branching processes that add the novelty with respect to BGWPs that the number of progenitors in each generation is determined by a random mechanism. Besides the theoretical motivation by itself, from a practical viewpoint, the interest in developing these results stems from the usefulness of this kind of limit theorems for sequences of branching processes in determining the asymptotic distributions of the weighted least squares estimators of the main parameters of the model. We will establish a set of sufficient conditions for the weak convergence of (suitably scaled) discrete-time, discrete-state controlled branching processes.