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Semigroup Stationary Processes and Spectral Representation
We present an extended definition of the second-order stationarity concept. This is based on the theory of harmonic analysis for semigroups with involution. It provides a spectral representation for a wide class of processes which are non-stationary in the usual weak sense, and allows miscellaneous...
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Published in: | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2003-10, Vol.9 (5), p.857-876 |
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container_title | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability |
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creator | Girardin, Valerie Senoussi, Rachid |
description | We present an extended definition of the second-order stationarity concept. This is based on the theory of harmonic analysis for semigroups with involution. It provides a spectral representation for a wide class of processes which are non-stationary in the usual weak sense, and allows miscellaneous spectral representation results to be unified. Many applications are given to illustrate the concept. Most of these are already known, but some are new, such as the multiplicative-symmetric processes. We are less concerned with proving fundamental results than with opening up a new field of investigation for spectral representation of non-stationary processes. |
doi_str_mv | 10.3150/bj/1066418881 |
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We are less concerned with proving fundamental results than with opening up a new field of investigation for spectral representation of non-stationary processes.</description><subject>Covariance</subject><subject>Index sets</subject><subject>Inverted spectra</subject><subject>Karhunen Loeve expansion</subject><subject>Life Sciences</subject><subject>Mathematical functions</subject><subject>non-stationary processes</subject><subject>positive definite functions</subject><subject>Semigroups</subject><subject>semigroups with involution</subject><subject>Spectral index</subject><subject>spectral representation</subject><subject>Stationary processes</subject><subject>Stochastic processes</subject><issn>1350-7265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><recordid>eNplkMFLwzAUxnNQcE6P3jz06qHupUmTzIuMoU4oKNadS5q8aku3lKQT_O_t6JiIpwff-30f33uEXFG4ZTSFWdnMKAjBqVKKnpAJZSnEMhHpGTkPoQGgXAiYkLscN_WHd7suynvd126r_Xf06p3BEDBEemujvEPTe91Gb9h5DLgdwQtyWuk24OVhTsn68eF9uYqzl6fn5SKLDVOyj1OUIJQRhgpLK5EIplIzr0pGuZRgE8kZmsRYUUpAwbhOLRhbcajmpaKcsSm5H3M775qhCe5MW9ui8_Vm6Fo4XRfLdXZQD6Nsit_zh4SbMeFTt398q0VW7DVIhFQS-NeejUfWeBeCx-pooFDsX_sv-3rkm9A7f4QZG9aSsh8PcHc2</recordid><startdate>20031001</startdate><enddate>20031001</enddate><creator>Girardin, Valerie</creator><creator>Senoussi, Rachid</creator><general>International Statistics Institute / Bernoulli Society</general><general>Bernoulli Society for Mathematical Statistics and Probability</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0001-9934-3561</orcidid></search><sort><creationdate>20031001</creationdate><title>Semigroup Stationary Processes and Spectral Representation</title><author>Girardin, Valerie ; Senoussi, Rachid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c387t-5e7068c6c16d1f626385c9fb314770d2743ec2cd6b70e634a5d0cdf40f9b81433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Covariance</topic><topic>Index sets</topic><topic>Inverted spectra</topic><topic>Karhunen Loeve expansion</topic><topic>Life Sciences</topic><topic>Mathematical functions</topic><topic>non-stationary processes</topic><topic>positive definite functions</topic><topic>Semigroups</topic><topic>semigroups with involution</topic><topic>Spectral index</topic><topic>spectral representation</topic><topic>Stationary processes</topic><topic>Stochastic processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Girardin, Valerie</creatorcontrib><creatorcontrib>Senoussi, Rachid</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Girardin, Valerie</au><au>Senoussi, Rachid</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semigroup Stationary Processes and Spectral Representation</atitle><jtitle>Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability</jtitle><date>2003-10-01</date><risdate>2003</risdate><volume>9</volume><issue>5</issue><spage>857</spage><epage>876</epage><pages>857-876</pages><issn>1350-7265</issn><abstract>We present an extended definition of the second-order stationarity concept. 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subjects | Covariance Index sets Inverted spectra Karhunen Loeve expansion Life Sciences Mathematical functions non-stationary processes positive definite functions Semigroups semigroups with involution Spectral index spectral representation Stationary processes Stochastic processes |
title | Semigroup Stationary Processes and Spectral Representation |
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