Accession Number : AD0690552

Title :   AN INVARIANCE PRINCIPLE FOR REVERSED MARTINGALES.

Descriptive Note : Technical rept.,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Loynes,Robert M.

Report Date : JUN 1969

Pagination or Media Count : 16

Abstract : Let (X sub n: n = or > 1) be a martingale, and for each n construct a random function W sub n by plotting X sub k at t = E(X sub k) squared/E(X sub n) squared, (1 = or < k = or < n), and scaling. If the finite-dimensional distributions of W sub n converge to those of the Wiener process W, then W sub n approaches W. Analogously, if (X sub n: n = or > 1) is a reverse martingale, construct W sub n by plotting X Sub k >(k = or n) at appropriate points; the same result holds. Sufficient conditions for the required convergence, and applications, are given for the reversed martingale case. (Author)

Descriptors :   (*STOCHASTIC PROCESSES, SEQUENCES(MATHEMATICS)), INVARIANCE, PROBABILITY, MEASURE THEORY, CONVERGENCE, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE