B1685
Title: Fluctuation limit theorem of critical controlled branching processes using limit theorems for martingale differences
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: Controlled branching processes are stochastic processes appropriate to model generation sizes in population dynamics studies where a control on the growth of population size is necessary for each generation. The main aim is to provide a Feller diffusion approximation for critical controlled branching processes. Previously, the result has been proved by using operator semigroup convergence theorems. An alternative proof is now provided making use of limit theorems for martingale differences. From a practical viewpoint, the interest in developing this result stems from its usefulness in determining the asymptotic distributions of estimators of the main parameters of a controlled branching process.
