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On spatial thinning-replacement processes based on Voronoi cells

Part of: Markov processes Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

K. A. Borovkov  and
D. A. Odell
K. A. Borovkov*
Affiliation:
The University of Melbourne
D. A. Odell*
Affiliation:
MASCOS
*
∗ Postal address: Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia. Email address: [email protected]
∗∗ Postal address: MASCOS, 139 Barry Street, Carlton, VIC 3010, Australia.
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Abstract

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We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is then removed, and a new random point is added to the configuration. The dynamics are simple and intuitive and could be applied to modelling natural phenomena. We prove ergodicity of these processes under wide conditions.

Keywords

Point processVoronoi tessellationMarkov chainergodicity

MSC classification

Primary: 60G55: Point processes
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 60F99: None of the above, but in this section
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 39 , Issue 2 , June 2007 , pp. 293 - 306
Copyright
Copyright © Applied Probability Trust 2007 

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