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Central limit theorem for germination-growth models in ℝd with non-Poisson locations

Part of: Stochastic processes Geometric probability and stochastic geometry Limit theorems

Published online by Cambridge University Press:  01 July 2016

S. N. Chiu  and
M. P. Quine
S. N. Chiu*
Affiliation:
Hong Kong Baptist University
M. P. Quine*
Affiliation:
University of Sydney
*
∗ Postal address: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong. Email address: [email protected]
∗∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia.
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Abstract

Seeds are randomly scattered in ℝd according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the potential germination time, the number of germinated seeds in a large region has an asymptotic normal distribution.

Keywords

Central limit theoremJohnson-Mehl tessellationm-dependent

MSC classification

Primary: 60G55: Point processes 60D05: Geometric probability and stochastic geometry 60F05: Central limit and other weak theorems
Secondary: 60G60: Random fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 33 , Issue 4 , December 2001 , pp. 751 - 755
Copyright
Copyright © Applied Probability Trust 2001 

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Footnotes

Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKBU/2075/98P) and an Australian Research Council grant.

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