Department of Mathematics
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 NL 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 (NL - E[NL])/[radical sign]var[NL] converges weakly to the standard normal distribution. In this paper a simpler argument is presented to prove this asymptotic normality of NL for a more general class of linear Kolmogorov's birth-growth models.
Central limit theorem, Coverage, Inhomogeneous Poisson process, Johnson-Mehl tessellation, Kolmogorov's birth-growth model
Source Publication Title
Stochastic Processes and their Applications
@ 1997 Elsevier Science B.V. All rights reserved
Link to Publisher's Edition
Chiu, S. (1997). A central limit theorem for linear Kolmogorov's birth-growth models. Stochastic Processes and their Applications, 66 (1), 97-106. https://doi.org/10.1016/S0304-4149(96)00113-5