STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.
Abstract
A stochastic point process in R(n) is a triple (M,B,P) where M is the class of all countable sets in R(n) having no limit points, B is the smallest sigma-algebra on M which makes the functions N sub s (x), defined by N sub s (x) = the number of points of x in S where x belongs to M and S is a Borel set in R(n), measurable, and P is a probability measure on B. A variety of operations on point processes which yield new point processes can be defined e.g. superposition, deleting points, random translations of points, and clustering of points. The sequence of processes produced by iteration of these operations on a specified point process will, under, very general conditions and for a wide class of point process including the stationary ones, converge to a mixture of Poisson processes. These results are established via a generalization of a classical limit theorem for Bernoulli trials. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 04, 1966
- Accession Number
- AD0629525
Entities
People
- Jay R. Goldman
Organizations
- Harvard University