
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 finitedimensional 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