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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2001-34
October 2001

Spatial Jump Processes and Perfect Simulation


Jesper Møller

Kasper K. Berthelsen


Spatial birth-and-death processes, spatial birth-and-catastrophe processes, and more general types of spatial jump processes are studied in detail. Particularly, various kinds of coupling constructions are considered, leading to some known and some new perfect simulation procedures for the equilibrium distributions of different types of spatial jump processes. These equilibrium distributions include many classical Gibbs point process models and a new class of models for spatial point processes introduced in the text.

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This paper has now been published in In Morphology of Condensed Matter, Eds. K. Mecke and D. Stoyan, Lecture Notes in Physics, Vol. 600, Springer-Verlag, 391 - 417 (2002)