AN INVARIANCE PRINCIPLE FOR REVERSED MARTINGALES.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1969
- Accession Number
- AD0690552
Entities
People
- Robert M. Loynes
Organizations
- University of North Carolina at Chapel Hill