• Limit Theorems for the Process of Exceedances in Large Populations
Ibrahim Rahimov and Husna Hasan
Abstract. We consider a discrete time branching process with n initial ancestors. Each of the ancestors generates a branching process with the same of spring distribution. Let be the number of ancestors having more than descendants at time t. We prove that can, in a weak sense, be approximated as by either a Poisson or a Binomial process depending on the criticality of the initial process.