Detection of spatial pattern through independence of thinned processes

Details Detection of spatial pattern through independence of thinned processes Detection of spatial pattern through independence of thinned processes

2001-03-16

arxiv.org/abs/math/0103104v1

Mathematics

Probability

11 pages, one figure

Scientific paper

10.1007/s11749-006-0012-z

Let N, N' and N'' be point processes such that N' is obtained from N by
homogeneous independent thinning and N''= N- N'. We give a new elementary proof
that N' and N'' are independent if and only if N is a Poisson point process. We
present some applications of this result to test if a homogeneous point process
is a Poisson point process.

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