Fourier expansions with polynomial terms for random processes
type: Item
instance of: scholarly article
title: Fourier expansions with polynomial terms for random processes
zbMATH Open document ID: 1347.60035
DOI: 10.1155/2015/763075
published in: Journal of Function Spaces
publication date: 2015-10-27T00:00:00Z
review text: Summary: 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 effects in our decomposition of a 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.
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 42A16
Mathematics Subject Classification ID: 42A61
Mathematics Subject Classification ID: 42B05
zbMATH DE Number: 6499109
zbMATH Keywords: random processes
zbMATH Keywords: Fourier expansions
author: Zhihua Zhang
Wikidata QID: Q59112891
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/763075
OpenAlex ID: W1921029614
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description: scientific article; zbMATH DE number 6499109