Galton-Watson theta-processes in a varying environment

Serik Sagitov; Yerakhmet Zhumayev

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arXiv · 2401.07860

Galton-Watson theta-processes in a varying environment

Serik Sagitov·Yerakhmet Zhumayev

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Abstract

We consider a special class of Galton-Watson theta-processes in a varying environment fully defined by four parameters, with two of them $(\theta,r)$ being fixed over time $n$, and the other two $(a_n,c_n)$ 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.

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Serik Sagitov, Yerakhmet Zhumayev. 2024-01-15. Galton-Watson theta-processes in a varying environment. https://arxiv.org/abs/2401.07860

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