Accession Number:

ADA018701

Title:

On the Functional Central Limit Theorem for Martingales

Descriptive Note:

Technical rept.

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1975-11-01

Pagination or Media Count:

21.0

Abstract:

Necessary and sufficient conditions for the functional central limit theorem for a double array of random variables are sought. It is argued that this is a martingale problem only if the variables truncated at some fixed point c are asymptotically a martingale difference array. Under this hypothesis, necessary and sufficient conditions for convergence in distribution to a Brownian motion are obtained when the normalization is given i by the sums of squares of the variables, ii by the conditional variances and iii by the variances. The results are proved by comparing the various normalizations with a natural normalization.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE