A central limit theorem for linear Kolmogorov's birth-growth models
type: Item
instance of: scholarly article
title: A central limit theorem for linear Kolmogorov's birth-growth models
zbMATH Open document ID: 0889.60048
DOI: 10.1016/S0304-4149(96)00113-5
author: Sung Nok Chiu
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: A birth-growth process of Kolmogorov's (1937) type is studied. Points are formed on \([0,L]\) according to a spatial-temporal Poisson process. Once the point \((x_i,t_i)\) is born, two bidirectional moving frontiers commence at \(x_i\). Each frontier moves at a constant speed until it meets an opposite one. The intervals passed over by moving frontiers are regarded as covered. New points continue to form on uncovered parts of \([0,L]\) until the whole interval is covered. Let \(N_L\) be the total number of points. \textit{M. P. Quine} and \textit{J. Robinson} [J. Appl. Probab. 27, No. 3, 499-509 (1990; Zbl 0718.60009)] proved the weak asymptotic normality of \(N_L\) as \(L\rightarrow \infty \). Under their approach the result is generalised, and a simpler proof is given.
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 1134808
zbMATH Keywords: point processes
zbMATH Keywords: central limit theorem
zbMATH Keywords: inhomogeneous Poisson process
zbMATH Keywords: birth-growth model
reviewed by: Viktor Beneš
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1134808