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Modelling random linear nucleation and growth by a Markov chain

Part of:Markov processesLimit theorems

Published online by Cambridge University Press:  14 July 2016

M. P. Quine and
J. S. Law
M. P. Quine*
Affiliation:
University of Sydney
J. S. Law*
Affiliation:
University of Sydney
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of ‘drops’ during times 1,2,…n is of the optimal ‘Berry–Esséen’ form, as n → ∞. We also establish a law of the iterated logarithm and a functional central limit theorem.

Keywords

Linear growth modelMarkov chainBerry–EsséenLILfunctional CLT

MSC classification

Primary:60J10: Markov chains (discrete-time Markov processes on discrete state spaces)60F05: Central limit and other weak theorems
Secondary:60F17: Functional limit theorems; invariance principles

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999, pp. 273 - 278
Copyright
Copyright © Applied Probability Trust 1999 

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