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.
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