A central limit theorem for linear Kolmogorov's birth-growth models

[摘要] A Poisson process in space-time is used to generate a linear Kolmogorov's birth-growth model. Points start to form on [0,L] at time zero. Each newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over parts of [0,L]. The whole interval will eventually be passed over by the moving frontiers. Let N-L be the total number of points formed. Quine and Robinson (1990) showed that if the Poisson process is homogeneous in space-time, the distribution of (N-L - E[N-L])/root var[N-L] converges weakly to the standard normal distribution. In this paper a simpler argument is presented to prove this asymptotic normality of N-L for a more general class of linear Kolmogorov's birth-growth models.

[发布日期] 1997-02-01

[关键词] central limit theorem;coverage;inhomogeneous Poisson process;Johnson-Mehl tessellation;Kolmogorov's birth-growth model