Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

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.

Keywords

Central limit theorem, Coverage, Inhomogeneous Poisson process, Johnson-Mehl tessellation, Kolmogorov's birth-growth model

Publication Date

2-1997

Source Publication Title

Stochastic Processes and their Applications

Volume

66

Issue

1

Start Page

97

End Page

106

Publisher

Elsevier

Peer Reviewed

1

Copyright

@ 1997 Elsevier Science B.V. All rights reserved

DOI

10.1016/S0304-4149(96)00113-5

Link to Publisher's Edition

https://doi.org/10.1016/S0304-4149(96)00113-5

ISSN (print)

03044149

ISSN (electronic)

1879209X

Included in

Mathematics Commons

Share

COinS