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 ℝ’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.