On Conditions for Ergodicity of Stationary Processes in Terms of Higher Order Moments

Previous article On Conditions for Ergodicity of Stationary Processes in Terms of Higher Order MomentsA. N. ShiryaevA. N. Shiryaevhttps://doi.org/10.1137/1108049PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIn this paper the necessary and sufficient conditions are given for the ergodicity of stationary processes in terms of time and spectral moments of higher order (equations (2) and (4)).[1] V. P. Leonov, Application of the characteristic functional and semi-invariants to the ergodic theory of stationary processes, Dokl. Akad. Nauk SSSR, 133 (1960), 523–526, (In Russian.) Google Scholar[2] A. N. Shiryaev, Some problems in the spectral theory of higher-order moments. I, Theory Prob. Applications, 5, (1960), 265–284, (English translation.) 0109.36001 Google Scholar[3] A. Blanc-Lapierre and , Robert Fortet, Théorie des fonctions aléatoires. Applications à divers phénomènes de fluctuation, Masson et Cie, Paris, 1953xvi+693 MR0061780 0051.35702 Google Scholar[4] Ya. G. Sinai, On higher order spectral measures of ergodic stationary processes, Theory Prob. Applications, (), 429–436, this issue, (English translation.) 0143.19401 Google Scholar Previous article FiguresRelatedReferencesCited byDetails References14 March 2018 Cross Ref Retrieval of Higher Order Ocean Spectral Information From SunglintIEEE Transactions on Geoscience and Remote Sensing, Vol. 53, No. 1 Cross Ref An Introduction to Polyspectra9 November 2011 Cross Ref Quickest Detection in Multiple On–Off ProcessesIEEE Transactions on Signal Processing, Vol. 58, No. 12 Cross Ref References21 March 2005 Cross Ref Bibliography on higher-order statisticsSignal Processing, Vol. 60, No. 1 Cross Ref Ergodicity and fourth-order spectral momentsIEEE Transactions on Information Theory, Vol. 43, No. 4 Cross Ref Bispectrum estimation: A digital signal processing frameworkProceedings of the IEEE, Vol. 75, No. 7 Cross Ref Phase estimation using the bispectrumProceedings of the IEEE, Vol. 72, No. 10 Cross Ref Spectrum estimation and harmonic analysisProceedings of the IEEE, Vol. 70, No. 9 Cross Ref Some History Of The Study Of Higher-order Moments And Spectra Cross Ref Geometrical concepts in HOS Cross Ref Stationary Processes Cross Ref Volume 8, Issue 4| 1963Theory of Probability & Its Applications History Submitted:26 May 1962Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1108049Article page range:pp. 436-439ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics