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Critical Multitype Branching Processes with Random Migration

Author

Listed:
  • González Miguel

    (Departamento de Matemáticas, Facultad de Ciencias and Instituto de Computación Científica Avanzada, 16759 Universidad de Extremadura , Badajoz, Spain)

  • Martín-Chávez Pedro

    (Departamento de Matemáticas, Facultad de Ciencias, 197444 Universidad de Extremadura , Badajoz, Spain)

  • del Puerto Inés

    (Departamento de Matemáticas, Facultad de Ciencias and Instituto de Computación Científica Avanzada, 16759 Universidad de Extremadura , Badajoz, Spain)

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.

Suggested Citation

  • González Miguel & Martín-Chávez Pedro & del Puerto Inés, 2024. "Critical Multitype Branching Processes with Random Migration," Stochastics and Quality Control, De Gruyter, vol. 39(1), pages 51-58.
    • Handle: RePEc:bpj:ecqcon:v:39:y:2024:i:1:p:51-58:n:1004
    DOI: 10.1515/eqc-2024-0010
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