Accession Number : AD0782420

Title :   The Description of a Random Field by Means of Its Conditional Distribution.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF OPERATIONS RESEARCH HOUSE

Personal Author(s) : Jacobs,P. A.

Report Date : MAR 1974

Pagination or Media Count : 17

Abstract : Let T denote the d-dimensional integer lattice. Let X = (X(t); t belongs to T) be a process taking values on a countable space E with probability law P. The pair (X,P) is called a random field. For each finite subset J of T, let Q sub J denote the conditional distribution of (X(t); t belongs to J) given the values of X(t), t belongs to J. The collection Q = (Q sub J; J subset T) is called the conditional distribution of (X,P). A characterization is given for the collection of all random fields with a given conditional distribution Q. (Author)

Descriptors :   *Algebra, *Vector spaces, Probability density functions, Measure theory, Set theory, Theorems

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE