Thinning of a Point Process Over Time.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1976
- Accession Number
- ADA037491
Entities
People
- Richard F. Serfozo
Organizations
- Syracuse University