Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 154632, 8 pages
Research Article

Approximation of Second-Order Moment Processes from Local Averages

1School of Science, Tianjin University, Tianjin 300072, China
2Institute of TV and Image Information, Tianjin University, Tianjin 300072, China

Received 6 March 2009; Accepted 8 July 2009

Academic Editor: Jozef Banas

Copyright © 2009 Zhanjie Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We use local averages to approximate processes that have finite second-order moments and are continuous in quadratic mean. We also provide some insight and generalization of the connection between Bernstein polynomials and Brownian motion, which was investigated by Kowalski in 2006.