Theta-positive branching in varying environment
Sagitov S. Lindo A. Zhumayev Y.
2025Taylor and Francis Ltd.
Stochastics
2025
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.
Continuous time branching process , limit theorems , theta branching , varying environment
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Chalmers University and University of Gothenburg, Gothenburg, Sweden
University of Glasgow, Glasgow, United Kingdom
L. N. Gumilev Eurasian National University, Astana, Kazakhstan
Chalmers University and University of Gothenburg
University of Glasgow
L. N. Gumilev Eurasian National University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026