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

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 .d 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.