New York Journal of Mathematics
Volume 4 (1998) 75-82


M. A. Akcoglu, J. R. Baxter, D. M. Ha, and R. L. Jones

Approximation of L2-Processes by Gaussian Processes

Published: May 21, 1998
Keywords: L2-processes, Gaussian processes, Bourgain's entropy theorem
Subject: Primary: 28D99, Secondary: 60F99

Let T be an ergodic transformation of a nonatomic probability space, f an L2-function, and K≧1 an integer. It is shown that there is another L2-function g, such that the joint distribution of Tig, 1≦ i≦ K, is nearly normal, and such that the corresponding inner products (Tif,Tjf) and (Tig,Tjg) are nearly the same for 1≦ i,j≦ K. This result can be used to give a simpler and more transparent proof of an important special case of an earlier theorem [3], which was a refinement of Bourgain's entropy theorem [9].


Research supported by NSERC and NSF Grants

Author information

M. A. Akcoglu:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada

J. R. Baxter:
School of Mathematics, University of Minneapolis, Minneapolis, MN 55455, USA

D. M. Ha:
Department of Mathematics, Middle East Technical Unversity, 06531 Ankara, Turkey

R. L. Jones:
Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago, IL 60614