Theta-positive branching in varying environment

Serik Sagitov; Alexey Lindo; Yerakhmet Zhumayev

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arXiv · 2303.04230

Theta-positive branching in varying environment

Serik Sagitov·Alexey Lindo·Yerakhmet Zhumayev

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Abstract

Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough investigation of such processes within a continuous-time framework, assuming that the reproduction law of individuals adheres to a specific parametric form for the probability generating function. Our six clear-cut limit theorems support the notion of recognizing five distinct asymptotical regimes for branching in varying environments: supercritical, asymptotically degenerate, critical, strictly subcritical, and loosely subcritical.

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Serik Sagitov, Alexey Lindo, Yerakhmet Zhumayev. 2023-03-07. Theta-positive branching in varying environment. https://arxiv.org/abs/2303.04230

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