AN INVARIANCE PRINCIPLE FOR REVERSED MARTINGALES.

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 EX sub k squaredEX 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