Limit theorems for the time of completion of Johnson-Mehl tessellations

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Johnson–Mehl tessellations can be considered as the results of spatial birth–growth processes. It is interesting to know when such a birth–growth process is completed within a bounded region. This paper deals with the limiting distributions of the time of completion for various models of Johnson–Mehl tessellations in ℝd and k-dimensional sectional tessellations, where 1 ≦ k < d, by considering asymptotic coverage probabilities of the corresponding Boolean models. Random fractals as the results of birth–growth processes are also discussed in order to show that a birth–growth process does not necessarily lead to a Johnson–Mehl tessellation.
Original languageEnglish
Pages (from-to)889-910
Number of pages22
JournalAdvances in Applied Probability
Issue number4
Publication statusPublished - Dec 1995

User-Defined Keywords

  • Boolean Models
  • Coverage
  • Extreme Value Distributions
  • Johnson–Mehl Tessellations
  • Fractals
  • Stochastic Geometry


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