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Galton–Watson Theta-Processes in a Varying Environment

Author

Listed:
  • Sagitov Serik

    (Department of Mathematical Sciences, [11248]Chalmers University of Technology; and the University of Gothenburg, Gothenburg, Sweden)

  • Zhumayev Yerakhmet

    (Department of Mathematics, [112657]L. N. Gumilev Eurasian National University, Astana, Kazakhstan)

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.

Suggested Citation

  • Sagitov Serik & Zhumayev Yerakhmet, 2024. "Galton–Watson Theta-Processes in a Varying Environment," Stochastics and Quality Control, De Gruyter, vol. 39(1), pages 25-39.
    • Handle: RePEc:bpj:ecqcon:v:39:y:2024:i:1:p:25-39:n:1002
    DOI: 10.1515/eqc-2024-0001
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