Аннотация
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 ) {(\theta,r)} being fixed over time n, and the other two ( a n , c n ) {(a_{n},c_{n})} 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.