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The prolific backbone for supercritical superprocesses

Author

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  • Berestycki, J.
  • Kyprianou, A.E.
  • Murillo-Salas, A.

Abstract

We develop an idea of Evans and O'Connell (1994) [13], Engländer and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called 'backbone' decomposition for supercritical superprocesses. Our results also complement a related result for critical (1+[beta])-superprocesses given in Etheridge and Williams (2003) [11]. Our approach relies heavily on the use of Dynkin-Kuznetsov -measures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:6:p:1315-1331
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. Hénard, Olivier, 2013. "Change of measure in the lookdown particle system," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2054-2083.
    3. Li, Zenghu & Zhu, Yaping, 2022. "Survival probability for super-Brownian motion with absorption," Statistics & Probability Letters, Elsevier, vol. 186(C).

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    1. 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.
    2. Li, Zenghu & Zhu, Yaping, 2022. "Survival probability for super-Brownian motion with absorption," Statistics & Probability Letters, Elsevier, vol. 186(C).
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