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Point process limits of lattice processes

Published online by Cambridge University Press:  14 July 2016

Julian Besag ,
Robin Milne  and
Stan Zachary
Julian Besag*
Affiliation:
University of Durham
Robin Milne*
Affiliation:
University of Western Australia
Stan Zachary*
Affiliation:
Heriot-Watt University
*
∗Postal address: Department of Mathematics, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, U.K.
∗∗Postal address: Department of Mathematics, University of Western Australia, Nedlands, WA 6009, Australia.
∗∗∗Postal address: Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Riccarton, Currie, Edinburgh EH14 4AS, U.K.
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Abstract

Starting from a suitable sequence of auto-Poisson lattice schemes, it is shown that (almost) any purely inhibitory pairwise-interaction point process can be obtained in the limit. Further pairwise-interaction processes are obtained as limits of sequences of auto-logistic lattice schemes.

Keywords

SPATIAL POINT PROCESSAUTO-POISSON SCHEMEAUTO-LOGISTIC SCHEMESTRAUSS PROCESSPAIRWISE-INTERACTION PROCESSINHIBITORY POINT PROCESSHARD-CORE POINT PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 210 - 216
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Work done while this author was visiting the University of Durham.

References

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