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

Víctor Manuel Rivero ()

Journal of Theoretical Probability, 2003, vol. 16, issue 1, 277-307

Abstract: 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.

Keywords: Poisson point process; extremal process; regenerative sets; subordinators; fractal dimensions (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1022247025107

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