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Lifetime and compactness of range for super-Brownian motion with a general branching mechanism

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  • Sheu, Yuan-Chung

Abstract

Let X be a super-Brownian motion with a general (time-space) homogeneous branching mechanism. We study a relation between lifetime and compactness of range for X. Under a restricted condition on the branching mechanism, we show that the set X survives is the same as that the range of X is unbounded. (For [alpha]-branching super-Brownian motion, 1

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:70:y:1997:i:1:p:129-141
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    Cited by:

    1. 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.
    2. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2021. "The extremal process of super-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 1-34.
    3. Li, Zenghu & Zhu, Yaping, 2022. "Survival probability for super-Brownian motion with absorption," Statistics & Probability Letters, Elsevier, vol. 186(C).
    4. Engländer, János & Fleischmann, Klaus, 2000. "Extinction properties of super-Brownian motions with additional spatially dependent mass production," Stochastic Processes and their Applications, Elsevier, vol. 88(1), pages 37-58, July.
    5. 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.

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