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Spatial Point Processes and the Projection Method

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In and Out of Equilibrium 2

Part of the book series: Progress in Probability ((PRPR,volume 60))

Abstract

The projection method obtains non-trivial point processes from higher-dimensional Poisson point processes by constructing a random subset of the higher-dimensional space and projecting the points of the Poisson process lying in that set onto the lower-dimensional region. This paper presents a review of this method related to spatial point processes as well as some examples of its applications. The results presented here are known for sometime but were not published before. Also, we present a backward construction of general spatial pure-birth processes and spatial birth and death processes based on the projection method that leads to a perfect simulation scheme for some Gibbs distributions in compact regions.

This research is partially supported by NSF under grant DMS 05-03983 and CNPq grant 301054/1993-2.

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Author information

Authors and Affiliations

  1. Departmento de Estatística, IMECC-UNICAMP, Caixa Postal 6065, 13.081-970, Campinas, SP, Brazil

    Nancy L. Garcia

  2. Department of Mathematics and Statistics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI, 53706, USA

    Thomas G. Kurtz

Authors
  1. Nancy L. Garcia
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  2. Thomas G. Kurtz
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Editor information

Editors and Affiliations

  1. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110 Jardim Botanico, CEP 22460-320, Rio de Janeiro, RJ, Brasil

    Vladas Sidoravicius

  2. Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150 Urca, 22290-180, Rio de Janeiro, RJ, Brasil

    Maria Eulália Vares

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Garcia, N.L., Kurtz, T.G. (2008). Spatial Point Processes and the Projection Method. In: Sidoravicius, V., Vares, M.E. (eds) In and Out of Equilibrium 2. Progress in Probability, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8786-0_13

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