Accession Number : AD0779066

Title :   On Symmetrically Distributed Random Measures,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Kallenberg,Olav

Report Date : OCT 1973

Pagination or Media Count : 26

Abstract : A random measure xi defined on some measurable space (S,S) is said to be symmetrically distributed with respect to some fixed measure omega on S, if the distribution of (xi A1,..., xi Ak) for K an element of N and dispoint A1,..., Ak an element of S only depends on (omega A1,..., omega Ak). The first purpose of the present paper is to extend to such random measures (and then even improve) the results on convergence in distribution and almost surely, previously given for random processes on the line with interchangeable increments, and further to give a new proof of the basic canonical representation. The second purpose is to extend a well-known theorem of Slivnyak by proving that the symmetrically distributed random measures may be characterized by a simple invariance property of the corresponding Palm distributions. (Author)

Descriptors :   *Measure theory, *Distribution functions, Topology, Random variables, Convergence, Theorems

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE