Critical Multitype Branching Processes with Random Migration-Reference-Cited by-同舟云学术

Critical Multitype Branching Processes with Random Migration

Published:2024-05-04 Issue:1 Volume:39 Page:51-58
ISSN:2367-2390
Container-title:Stochastics and Quality Control
language:en
Short-container-title:

Author:

González Miguel¹^ORCID,Martín-Chávez Pedro²^ORCID,del Puerto Inés¹^ORCID

Affiliation:

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

2. Departamento de Matemáticas , Facultad de Ciencias , 197444 Universidad de Extremadura , Badajoz , Spain

Abstract

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.

Funder

Agencia Estatal de Investigación

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/eqc-2024-0010/pdf

Reference17 articles.

1. M. Barczy, M. González, P. Martín-Chávez, and I. del Puerto, Diffusion approximation of critical controlled multi-type branching processes, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 (2024), Article No. 101.

2. Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer Texts Statist., Springer, New York, 1997.

3. E. E. Dyakonova, Branching processes that are close to critical with migration (in Russian), Teor. Veroyatnost. i Primenen. 41 (1996), no. 1, 186-192

4. translation in Theory Probab. Appl. 41 (1996), 186-192.

5. M. González, R. Martínez and M. Mota, On the unlimited growth of a class of homogeneous multitype Markov chains, Bernoulli 11 (2005), no. 3, 559–570.