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Stochastic equations and limit results for some two-type branching models

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  • Kaj, Ingemar
  • Tahir, Daniah

Abstract

A class of binary state, asymmetric, continuous time Markov branching processes are analyzed under supercritical conditions. Stochastic equations are provided, and limit results for the long time asymptotics as well as for the behavior of the model under rescaling are reviewed. Extensions are presented for model variations, such as population size dependence, with the purpose of promoting further use of these models for applications.

Suggested Citation

  • Kaj, Ingemar & Tahir, Daniah, 2019. "Stochastic equations and limit results for some two-type branching models," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 35-46.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:35-46
    DOI: 10.1016/j.spl.2019.02.011
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    References listed on IDEAS

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    1. Xu, Wei, 2014. "Parameter estimation in two-type continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 124-134.
    2. Ma, Rugang, 2014. "Stochastic equations for two-type continuous-state branching processes with immigration and competition," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 83-89.
    3. D. Anderson & J. Blom & M. Mandjes & H. Thorsdottir & K. Turck, 2016. "A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 153-168, March.
    4. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
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