 

M. A. Akcoglu, J. R. Baxter, D. M. Ha, and R. L. Jones
Approximation of L_{2}Processes by Gaussian Processes


Published: 
May 21, 1998 
Keywords: 
L_{2}processes, Gaussian processes, Bourgain's entropy theorem 
Subject: 
Primary: 28D99, Secondary: 60F99 


Abstract
Let T be an ergodic transformation of a nonatomic probability space, f an
L_{2}function, and K≧1 an integer. It is shown that there is another
L_{2}function g, such that the joint distribution of T^{i}g,
1≦ i≦ K, is nearly
normal, and such that the corresponding inner products (T^{i}f,T^{j}f) and
(T^{i}g,T^{j}g) 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].


Acknowledgements
Research supported by NSERC and NSF Grants


Author information
M. A. Akcoglu:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A1, Canada
akcoglu@math.toronto.edu
J. R. Baxter:
School of Mathematics, University of Minneapolis, Minneapolis, MN 55455, USA
baxter@math.umn.edu
D. M. Ha:
Department of Mathematics, Middle East Technical Unversity, 06531 Ankara, Turkey
hadzung@arf.math.metu.edu.tr
R. L. Jones:
Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago, IL 60614
http://www.depaul.edu/~rjones/

