Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series
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 e...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/265031 |
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| _version_ | 1832567302645612544 |
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| author | Zhihua Zhang |
| author_facet | Zhihua Zhang |
| author_sort | Zhihua Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-42e1e73496d44cf1b287f1376bf2b69a |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-42e1e73496d44cf1b287f1376bf2b69a2025-02-03T01:01:51ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/265031265031Hyperbolic Cross Truncations for Stochastic Fourier Cosine SeriesZhihua Zhang0College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, ChinaBased 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.http://dx.doi.org/10.1155/2014/265031 |
| spellingShingle | Zhihua Zhang Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series The Scientific World Journal |
| title | Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series |
| title_full | Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series |
| title_fullStr | Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series |
| title_full_unstemmed | Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series |
| title_short | Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series |
| title_sort | hyperbolic cross truncations for stochastic fourier cosine series |
| url | http://dx.doi.org/10.1155/2014/265031 |
| work_keys_str_mv | AT zhihuazhang hyperboliccrosstruncationsforstochasticfouriercosineseries |