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

Sung Nok CHIU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

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])/√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.

Original languageEnglish
Pages (from-to)97-106
Number of pages10
JournalStochastic Processes and their Applications
Volume66
Issue number1
DOIs
Publication statusPublished - 1 Feb 1997

Scopus Subject Areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

User-Defined Keywords

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

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