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Dimensions of supercritical branching processes in varying environments

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  • Shieh, Narn-Rueih
  • Yu, Jinghu

Abstract

Let [not partial differential][Gamma] be the boundary of a family tree [Gamma] associated with a supercritical branching process in varying environments. In this paper, the Hausdorff dimension, the upper box dimension and the packing dimension of [not partial differential][Gamma] are computed explicitly. In contrast to the (fixed environment) Galton-Watson case, the Hausdorff and upper box dimension may take different values.

Suggested Citation

  • Shieh, Narn-Rueih & Yu, Jinghu, 2004. "Dimensions of supercritical branching processes in varying environments," Statistics & Probability Letters, Elsevier, vol. 70(4), pages 299-308, December.
    • Handle: RePEc:eee:stapro:v:70:y:2004:i:4:p:299-308
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    References listed on IDEAS

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    1. Biggins, J. D. & D'Souza, J. C., 1993. "The supercritical Galton-Watson process in varying environments--Seneta-Heyde norming," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 237-249, November.
    2. D'Souza, J. C. & Biggins, J. D., 1992. "The supercritical Galton-Watson process in varying environments," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 39-47, August.
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