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Critical branching processes with immigration

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Workshop on Branching Processes and Their Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 197))

Abstract

In this paper we give a survey on some results concerning critical and nearly critical Galton–Watson branching processes with immigration. As a byproduct of a general limit theorem for weak convergence of step processes of martingale differences towards a diffusion process, functional limit theorems can be proved for different models. The limit process is either a squared Bessel process or an Ornstein–Uhlenbeck type process. The asymptotic behavior of conditional least squares estimator of the offspring mean will also be described. The results are applied in the theory of integer-valued autoregression as well.

Mathematics Subject Classification (2000): 60J80, 60F17, 62F12

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Acknowledgements

This research was supported by the Hungarian Scientific Research Fund under Grant No. OTKA T-079128.

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Authors and Affiliations

  1. Faculty of Informatics, University of Debrecen, Pf.12, Debrecen, H-4010, Hungary

    Márton Ispány & Gyula Pap

Authors
  1. Márton Ispány
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  2. Gyula Pap
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Corresponding authors

Correspondence to Márton Ispány or Gyula Pap .

Editor information

Editors and Affiliations

  1. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Miguel González Velasco

  2. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Inés M. Puerto

  3. Universidad de Extremadura, Avda. Virgen del Puerto, Plasencia, 10600, Spain

    Rodrigo Martínez

  4. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Molina

  5. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Mota

  6. Facultad de Veterinaria, Universidad de Extradura, Avda Universidad s/n, Caceres, 10071, Spain

    Alfonso Ramos

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Ispány, M., Pap, G. (2010). Critical branching processes with immigration. In: González Velasco, M., Puerto, I., Martínez, R., Molina, M., Mota, M., Ramos, A. (eds) Workshop on Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11156-3_10

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