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The Scientific World Journal
Volume 2014, Article ID 265031, 13 pages
Research Article

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China

Received 24 February 2014; Accepted 8 July 2014; Published 24 July 2014

Academic Editor: Wenchun Jiang

Copyright © 2014 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.


Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions.