Fourier Expansions with Polynomial Terms for Random Processes

Fourier Expansions with Polynomial Terms for Random Processes

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 a...

Full description

Bibliographic Details
Main Author: Zhihua Zhang
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2015/763075
id doaj-625357e87c6241bcb716ee0eb136400f
record_format Article
spelling doaj-625357e87c6241bcb716ee0eb136400f2020-11-24T22:22:17ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/763075763075Fourier Expansions with Polynomial Terms for Random ProcessesZhihua Zhang0College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, ChinaBased 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.http://dx.doi.org/10.1155/2015/763075
collection DOAJ
language English
format Article
sources DOAJ
author Zhihua Zhang
spellingShingle Zhihua Zhang
Fourier Expansions with Polynomial Terms for Random Processes
Journal of Function Spaces
author_facet Zhihua Zhang
author_sort Zhihua Zhang
title Fourier Expansions with Polynomial Terms for Random Processes
title_short Fourier Expansions with Polynomial Terms for Random Processes
title_full Fourier Expansions with Polynomial Terms for Random Processes
title_fullStr Fourier Expansions with Polynomial Terms for Random Processes
title_full_unstemmed Fourier Expansions with Polynomial Terms for Random Processes
title_sort fourier expansions with polynomial terms for random processes
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/763075
work_keys_str_mv AT zhihuazhang fourierexpansionswithpolynomialtermsforrandomprocesses
_version_ 1725768902101696512

Similar Items