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A spatial Markov property for nearest-neighbour Markov point processes

Published online by Cambridge University Press:  14 July 2016

W. S. Kendall
W. S. Kendall*
Affiliation:
University of Warwick
*
∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

Nearest-neighbour Markov point processes were introduced by Baddeley and Møller (1989) as generalizations of the Markov point processes of Ripley and Kelly. This note formulates and discusses a spatial Markov property for these point processes.

Keywords

CONNECTED NEIGHBOURSDIRICHLET NEIGHBOURSMARKOV PARTITIONRECTANGULAR NEIGHBOURSSPATIAL MARKOV PROPERTYSPLITTING BOUNDARYSPLITTING FIELDSTOCHASTIC GEOMETRY
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 767 - 778
Copyright
Copyright © Applied Probability Trust 1990 

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References

Baddeley, A. and Møller, J. (1989) Nearest-neighbour Markov point processes and random sets. Internat. Statist. Rev. 57, 89–121.Google Scholar
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Øksendal, B. (1985) Stochastic Differential Equations. Springer-Verlag, New York.Google Scholar
Ripley, B. D. and Kelly, F. P. (1977) Markov point processes. J. London Math. Soc. 15, 188–192.Google Scholar
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