Stochastic Modeling and Environmental Change
Published Online: 15 SEP 2006
Copyright © 2002 John Wiley & Sons, Ltd
Encyclopedia of Environmetrics
How to Cite
Çinlar, E. 2006. Poisson process. Encyclopedia of Environmetrics. 4.
- Published Online: 15 SEP 2006
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.