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A Markov construction for a multidimensional point process

Published online by Cambridge University Press:  14 July 2016

Valerie Isham
Valerie Isham*
Affiliation:
Imperial College, London
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Abstract

A sequence of finite point processes {Pn} is constructed in using a Markov sequence of points. Essentially, in the process Pn consisting of n events, the coordinates of these events are simply the first n points of a Markov sequence suitably scaled so that the average density of the process is independent of n. The second-order properties of Pn are discussed and sufficient conditions are found for Pn to converge in distribution to a Poisson process as n →∞. A simple example involving the cardioid distribution is described.

Keywords

MULTIDIMENSIONAL POINT PROCESSFINITE POINT PROCESSMARKOV SEQUENCECARDIOID DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 507 - 515
Copyright
Copyright © Applied Probability Trust 1977 

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References

Daley, D. J. and Vere-Jones, D. (1972) A summary of the theory of point processes. In Stochastic Point Processes , ed. Lewis, P.A.W., Wiley, New York, 299–393.Google Scholar
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