Accession Number : AD0629525

Title :   STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS

Personal Author(s) : Goldman,Jay R.

Report Date : 04 FEB 1966

Pagination or Media Count : 54

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)

Descriptors :   (*STOCHASTIC PROCESSES, THEOREMS), (*THEOREMS, STOCHASTIC PROCESSES), MEASURE THEORY

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE