Accession Number : ADA186433

Title :   Strong Representation of Weak Convergence.

Descriptive Note : Technical rept. Sep 86-Sep 87,

Corporate Author : NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Bai, Z D ; Liang, W Q ; Vervaat, W

PDF Url : ADA186433

Report Date : Jun 1987

Pagination or Media Count : 8

Abstract : This result is proved. If sub n is a separable metric space for nor = infinity, phi sub n: S sub n approaches limit of S sub infinity is measurable for sub infinity, X sub n is an S sub n valued random variable for nor = infinity and phi sub n (X sub n) approaches limit of sub x sub infinity in S sub infinity, then there exists S sub n valued random variables X sub n such that X sub n = d sub x sub n for nor = infinity and phi sub n (X sub n) approaches limit of X sub infinity wpl. Conditions on S sub n and phi sub n are presented that allow a construction in the context of Polish spaces.

Descriptors :   *WEAK CONVERGENCE, *MATRIX THEORY, *PROBABILITY DISTRIBUTION FUNCTIONS, LIMITATIONS, RANDOM VARIABLES

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE