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Journal of Function Spaces
Volume 2015, Article ID 763075, 12 pages
http://dx.doi.org/10.1155/2015/763075
Research Article

Fourier Expansions with Polynomial Terms for Random Processes

1College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China
2Joint Center for Global Change Studies, Beijing 100875, China

Received 8 October 2014; Accepted 23 December 2014

Academic Editor: Feyzi Başar

Copyright © 2015 Zhihua Zhang. 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.

Abstract

Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also new for deterministic functions.