Galton–Watson Theta-Processes in a Varying Environment-Reference-Cited by-同舟云学术

Galton–Watson Theta-Processes in a Varying Environment

Published:2024-01-30 Issue:1 Volume:39 Page:25-39
ISSN:2367-2390
Container-title:Stochastics and Quality Control
language:en
Short-container-title:

Author:

Sagitov Serik¹^ORCID,Zhumayev Yerakhmet²

Affiliation:

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

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

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/eqc-2024-0001/pdf

Reference12 articles.

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