CENTRAL LIMIT THEORY FOR THE NUMBER OF SEEDS IN A GROWTH MODEL IN Rd WITH INHOMOGENEOUS POISSON ARRIVALS
成果类型：
Article
署名作者：
Chiu, S. N.; Quine, M. P.
署名单位：
Hong Kong Baptist University; University of Sydney
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1997
页码：
802-814
关键词：
摘要：
A Poisson point process Psi in d-dimensional Euclidean space and in time is used to generate a birth-growth model: seeds are born randomly at locations x(i) in R-d at times t(i) is an element of [0, infinity). Once a seed is born, it begins to create a cell by growing radially in all directions with speed nu > 0. Points of Psi 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.