Accession Number : AD0666557

Title :   WEAK CONVERGENCE OF PROBABILITY MEASURES ON PRODUCT SPACES WITH APPLICATIONS TO SUMS OF RANDOM VECTORS,

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Iglehart,Donald L.

Report Date : 04 MAR 1968

Pagination or Media Count : 28

Abstract : Let C superscript k be the product of k copies of C(0,1), the space of continuous functions on (0,1) with the uniform metric, and D superscript k the product of k copies of D(0,1), the space of right continuous functions on (0,1) having left limits with the Skorohod metric. Necessary and sufficient conditions are obtained for the weak convergence of a sequence of probability measures (Pn) on C superscript k (or D superscript k) to a probability measure P. These results are then applied to obtain functional central limit theorems for sums of random vectors. The random vectors considered are either independent and identically distributed or stationary phi-mixing. Extensions to the case of sums of a random number of random variables are also treated. (Author)

Descriptors :   (*MEASURE THEORY, RANDOM VARIABLES), SET THEORY, TOPOLOGY, INVARIANCE, CONVERGENCE, PROBABILITY, SEQUENCES(MATHEMATICS), STATISTICAL PROCESSES, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE