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.
Funding source: Agencia Estatal de Investigación
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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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- 80th Jubilee of Professor Nikolay Yanev
- My 55 Years in Stochastics
- On Subcritical Markov Branching Processes with a Specified Limiting Conditional Law
- Galton–Watson Theta-Processes in a Varying Environment
- Population Dependent Two-Sex Branching Process with Random Mating and Overlapping Generations
- Critical Multitype Branching Processes with Random Migration
- Branching Processes Under Nonstandard Conditions
Artikel in diesem Heft
- Frontmatter
- 80th Jubilee of Professor Nikolay Yanev
- My 55 Years in Stochastics
- On Subcritical Markov Branching Processes with a Specified Limiting Conditional Law
- Galton–Watson Theta-Processes in a Varying Environment
- Population Dependent Two-Sex Branching Process with Random Mating and Overlapping Generations
- Critical Multitype Branching Processes with Random Migration
- Branching Processes Under Nonstandard Conditions