Central limit theory for the number of seeds in a growth model in \boldR\spd with inhomogeneous Poisson arrivals

A Poisson point process . in d-dimensional Euclidean space and in time is used to generate a birth-growth model: seeds are born randomly at locations xi in Rd at times ti.[0,.). Once a seed is born, it begins to create a cell by growing radially in all directions with speed v>0. Points of . contained in such cells are discarded, that is, thinned.We study the asymptotic distribution of the number of seeds in a region, as the volume of the region tends to infinity. When d=1, we establish conditions under which the evolution over time of the number of seeds in a region is approximated by a Wiener process. When d.1, we give conditions for asymptotic normality. Rates of convergence are given in all cases.