Galton–Watson Theta-Processes in a Varying Environment

Abstract

We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them (θ, r) being fixed over time n, and the other two (an , cn) characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.