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Convergence of spatial birth-and-death processes

Published online by Cambridge University Press:  24 October 2008

H. W. Lotwick  and
B. W. Silverman
H. W. Lotwick
Affiliation:
University of Bath
B. W. Silverman
Affiliation:
University of Bath
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Abstract

Some models for spatial point processes are difficult to simulate directly and are most easily realized as the equilibrium distribution of certain spatial-temporal Markov processes. This paper examines the convergence of such processes, concentrating mainly on the ‘hard core’ case when the points represent the centres of non-overlapping discs. Coupling methods from the theory of Markov chains are used to establish sufficient conditions for the processes to converge to the required equilibrium, and to give a lower bound on the rate of convergence. One technique used is to couple processes when they become close in a suitable metric.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 155 - 165
Copyright
Copyright © Cambridge Philosophical Society 1981

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