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Critical Multitype Branching Processes with Random Migration

  • Miguel González ORCID logo , Pedro Martín-Chávez ORCID logo und Inés del Puerto ORCID logo EMAIL logo
Veröffentlicht/Copyright: 4. Mai 2024
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Abstract

The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton–Watson process with migration introduced in [N. M. Yanev and K. V. Mitov, Controlled branching processes: The case of random migration, C. R. Acad. Bulgare Sci. 33 1980, 4, 473–475]. We focus our attention in what we call the critical case. Sufficient conditions are provided for the process to have unlimited growth or not. Furthermore, using suitable normalizing sequences, we study the asymptotic distribution of the process. Finally, we obtain a Feller-type diffusion approximation.

MSC 2020: 60J80

Award Identifier / Grant number: PID2019-108211GB-I00

Funding statement: The authors are supported by grant PID2019-108211GB-I00 funded by MICIU/AEI/10.13039/501100011033. Pedro Martín-Chávez is also grateful to the Ministerio de Ciencias, Innovación y Universidades for support from a predoctoral fellowship Grant No. FPU20/06588.

Acknowledgements

We would like to thank the referee for her/his comments that helped us improve the paper.

References

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Received: 2024-03-15
Revised: 2024-04-23
Accepted: 2024-04-23
Published Online: 2024-05-04
Published in Print: 2024-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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