Thinning of a Point Process Over Time.
SYRACUSE UNIV N Y DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
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Thinning of a point process refers to the procedure in which points are randomly placed in a region and then they are deleted according to some rule. The aim is to answer questions such as 1 how can the random placement and detection of points be described mathematically 2 what types of thinned processes arise from various thinning rules 3 how much thinning is needed for a desired rarefaction of points and 4 when does one reach diminishing returns in thinning. Examples of thinning procedures are debugging of computer programs and complex systems, filtration of particles from a solution, and the elimination of undesirable cell growth, insects or plants. This paper addresses several thinnings in which points are deleted over time. We show how the asymptotic behavior of a thinned process is equivalent to that of extreme values of the lives of its points under the thinning. We use this to describe independent, regenerative, and semi-stationary thinnings.
- Statistics and Probability