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A limit theorem for spatial point processes

Published online by Cambridge University Press:  01 July 2016

Steven P. Ellis
Steven P. Ellis*
Affiliation:
Massachusetts Institute of Technology
*
∗Present address: Department of Statistics, University of Rochester, Rochester, NY 14627, USA.
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Abstract

Spatial point processes are considered whose points are subjected to certain classes of affine transformations indexed by some variable, T. Under some hypotheses, for large T integrals with respect to such a point process behave approximately as if the process were Poisson. Under stronger hypotheses, the transformed process converges as a process to a Poisson process. The result gives the asymptotic distribution of certain density estimates.

Keywords

POISSON LIMITDENSITY ESTIMATION

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 646 - 659
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This work was partially supported by United States National Science Foundation Grants MCS 75-10376, PFR 79-01642, MCS 82-01732, and MCS 82-02122

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