Accession Number : AD0690491

Title :   THE EQUIVALENCE OF FUNCTIONAL CENTRAL LIMIT THEOREMS FOR COUNTING PROCESSES AND ASSOCIATED PARTIAL SUMS.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH

Personal Author(s) : Iglehart,Donald L. ; Whitt,Ward

Report Date : JUN 1969

Pagination or Media Count : 18

Abstract : Let (u sub n, n = or > 1) be a sequence of nonnegative random variables, not necessarily independent or identically distributed, with an associated counting process (N(t), t = or >), defined by N(t) = max (k: u sub 1 + ... + u sub k = or < t), u sub 1 = or < t; N(t) = 0, u sub 1 > t. It is shown that functional central limit theorems (invariance principles) for N(t) are equivalent to corresponding statements for the sequence of partial sums of the u sub n's. (Author)

Descriptors :   (*MEASURE THEORY, COUNTING METHODS), (*PROBABILITY, THEOREMS), STATISTICAL PROCESSES, QUEUEING THEORY, INVARIANCE

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE