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Poisson process

Stochastic Modeling and Environmental Change

  1. Erhan Çinlar

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vap023

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Çinlar, E. 2006. Poisson process. Encyclopedia of Environmetrics. 4.

Author Information

  1. Princeton University, NJ, USA

Publication History

  1. Published Online: 15 SEP 2006

Abstract

Point processes are used as models for the configurations formed by the random positions of some species of particles in some space; the terms ‘particle’ and ‘position’ take different meanings in different applications. If the particles can be treated as indistinguishable, it is convenient to represent the point process by a random measure N, letting N(A) denote the number of particles in the set A, with A ranging over a suitable collection of subsets of the space involved. Poisson random measures (PRMs) (or processes) are the point processes par excellence: they are mathematically tractable and are applicable in a wide range of situations, either directly or after some transformations.