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Diffusion Approximation of Branching Processes in Semi-Markov Environment

Author

Listed:
  • Nikolaos Limnios

    (Sorbonne University Alliance)

  • Elena Yarovaya

    (Lomonosov Moscow State University)

Abstract

We consider continuous-time Markov branching processes in semi-Markov random environment and obtain diffusion approximation results for the near critical case. The problem of semi-Markov environment, presented here, is new and more interesting than the Markov case, since it includes many particular interesting cases: Markov, renewal, etc. The particular case of the Markov random environment of continuous-time branching process diffusion approximation results are obtained.

Suggested Citation

  • Nikolaos Limnios & Elena Yarovaya, 2020. "Diffusion Approximation of Branching Processes in Semi-Markov Environment," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1583-1590, December.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-020-09814-w
    DOI: 10.1007/s11009-020-09814-w
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    References listed on IDEAS

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    1. Wei, C. Z. & Winnicki, J., 1989. "Some asymptotic results for the branching process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 261-282, April.
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