Limit theorems for discrete multitype branching processes counted with a characteristic

Abstract

For a multitype Galton-Watson tree 𝕋, we consider the associated Crump-Mode-Jagers (CMJ) process (𝑍 Φ 𝑛 ) 𝑛∈N which counts all individuals in 𝕋, and the contribution of each individual to 𝑍 Φ 𝑛 is determined by a (random) characteristic Φ evaluated at the age of the corresponding particle at time 𝑛. The goal of this paper is to investigate multitype CMJ processes (𝑍 Φ 𝑛 ) 𝑛∈ℕ . We provide a precise limit theorem for such processes.