A central limit theorem for linear Kolmogorov's birth-growth models
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.
scientific article; zbMATH DE number 1134808