Galton–Watson Theta-Processes in a Varying Environment

Serik Sagitov, Yerakhmet Zhumayev

2024

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DOI 10.1515/eqc-2024-0001

Data confidence 70 medium

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Abstract

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.