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On Random Sets Connected to the Partial Records of Poisson Point Process

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  • Víctor Manuel Rivero

Abstract

Random intervals are constructed from partial records in a Poisson point process in ]0,∞[×]0,∞[. These are used to cover partially [0,∞[; the purpose of this work is to study the random set ℛ that is left uncovered. We show that ℛ enjoys the regenerative property and identify its distribution in terms of the characteristics of the Poisson point process. As an application we show that ℛ is almost surely a fractal set and we calculate its dimension.

Suggested Citation

  • Víctor Manuel Rivero, 2003. "On Random Sets Connected to the Partial Records of Poisson Point Process," Journal of Theoretical Probability, Springer, vol. 16(1), pages 277-307, January.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:1:d:10.1023_a:1022247025107
    DOI: 10.1023/A:1022247025107
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