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Limit theorems for the time of completion of Johnson-Mehl tessellations

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

Published online by Cambridge University Press:  01 July 2016

S. N. Chiu
S. N. Chiu*
Affiliation:
Freiberg University of Mining and Technology
*
* Present address: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
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Abstract

Johnson–Mehl tessellations can be considered as the results of spatial birth–growth processes. It is interesting to know when such a birth–growth process is completed within a bounded region. This paper deals with the limiting distributions of the time of completion for various models of Johnson–Mehl tessellations in ℝd and k-dimensional sectional tessellations, where 1 ≦ k < d, by considering asymptotic coverage probabilities of the corresponding Boolean models. Random fractals as the results of birth–growth processes are also discussed in order to show that a birth–growth process does not necessarily lead to a Johnson–Mehl tessellation.

Keywords

BOOLEAN MODELSCOVERAGEEXTREME VALUE DISTRIBUTIONSJOHNSON–MEHL TESSELLATIONSFRACTALSSTOCHASTIC GEOMETRY

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60G70: Extreme value theory; extremal processes
Secondary: 60F05: Central limit and other weak theorems 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 4 , December 1995 , pp. 889 - 910
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by a scholarship from DAAD, Postfach 200 404, D-53134 Bonn, Germany.

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