Estimation Problems in Branching Processes with Random Environments

Abstract

Estimators are given for the two main parameters of the branching process with random environments, namely, the mean of the environmental mean (the average number of offspring per individual) and the mean of the logarithm of the environmental mean. The latter parameter indicates the certain extinction or possible explosion of the process. The consistency and asymptotic normality of the estimators are shown in the context of Smith and Wilkinson. Consistent estimators are also given for the corresponding variances and thus confidence intervals are obtained for the two main parameters of the system.