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Backbone decomposition for continuous-state branching processes with immigration

Author

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  • Kyprianou, A.E.
  • Ren, Y.-X.

Abstract

In the spirit of Duquesne and Winkel (2007) and Berestycki et al. (2011), we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equivalent in law to a continuous-time Galton–Watson process with immigration (with Poissonian dressing). The result also helps to characterise the limiting backbone decomposition which is predictable from the work on consistent growth of Galton–Watson trees with immigration in Cao and Winkel (2010).

Suggested Citation

  • Kyprianou, A.E. & Ren, Y.-X., 2012. "Backbone decomposition for continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 139-144.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:139-144
    DOI: 10.1016/j.spl.2011.09.013
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    References listed on IDEAS

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    1. El Karoui, Nicole & Roelly, Sylvie, 1991. "Propriétés de martingales, explosion et représentation de Lévy--Khintchine d'une classe de processus de branchement à valeurs mesures," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 239-266, August.
    2. Sheu, Yuan-Chung, 1997. "Lifetime and compactness of range for super-Brownian motion with a general branching mechanism," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 129-141, October.
    3. Berestycki, J. & Kyprianou, A.E. & Murillo-Salas, A., 2011. "The prolific backbone for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1315-1331, June.
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