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Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

 

Zhihua Zhang

 

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

 

ABSTRACT

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.

 

PUBLISHED BY: SCIENTIFIC WORLD JOURNAL, 2014, 10.1155/2014/265031

 

SOURCE:  http://www.hindawi.com/journals/tswj/2014/265031/