Applebaum, D.B. (2016) Stationary Random Fields on the Unitary Dual of a Compact Group. In: Donati-Martin, C., Lejay, A. and Rouault, A., (eds.) Séminaire de Probabilités. Journées de Probabilités Lecture Notes in Mathematics, XLVIII . Springer International Publishing , pp. 469-480. ISBN 978-3-319-44464-2
Abstract
We generalise the notion of wide-sense stationarity from sequences of complex-valued random variables indexed by the integers, to fields of random variables that are labelled by elements of the unitary dual of a compact group. The covariance is positive definite, and so it is the Fourier transform of a finite central measure (the spectral measure of the field) on the group. Analogues of the Cramer and Kolmogorov theorems are extended to this framework. White noise makes sense in this context and so, for some classes of group, we can construct time series and investigate their stationarity. Finally we indicate how these ideas fit into the general theory of stationary random fields on hypergroups.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2016 Springer International Publishing Switzerland. This is an author produced version of a paper subsequently published in Lecture Notes in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 23 Feb 2017 15:37 |
Last Modified: | 19 Nov 2017 01:38 |
Published Version: | https://doi.org/10.1007/978-3-319-44465-9_18 |
Status: | Published |
Publisher: | Springer International Publishing |
Series Name: | Lecture Notes in Mathematics |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-319-44465-9_18 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:106775 |