A. N. Shiryaev, “On Conditions for Ergodicity of Stationary Processes in Terms of Higher Order Moments”, Teor. Veroyatnost. i Primenen., 8:4 (1963), 470–473; Theory Probab. Appl., 8:4 (1963), 436

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Teoriya Veroyatnostei i ee Primeneniya, 1963, Volume 8, Issue 4, Pages 470–473 (Mi tvp4694)

This article is cited in 13 scientific papers (total in 13 papers)

Short Communications

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

A. N. Shiryaev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Full-text PDF (447 kB) Citations (13)

Abstract: In 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)).

Received: 26.05.1962

English version:
Theory of Probability and its Applications, 1963, Volume 8, Issue 4, Pages 436–439
DOI: https://doi.org/10.1137/1108049

Document Type: Article

Language: Russian

Citation: A. N. Shiryaev, “On Conditions for Ergodicity of Stationary Processes in Terms of Higher Order Moments”, Teor. Veroyatnost. i Primenen., 8:4 (1963), 470–473; Theory Probab. Appl., 8:4 (1963), 436–439

Citation in format AMSBIB

\Bibitem{Shi63}

\by A.~N.~Shiryaev

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

\jour Teor. Veroyatnost. i Primenen.

\yr 1963

\vol 8

\issue 4

\pages 470--473

\mathnet{http://mi.mathnet.ru/tvp4694}

\transl

\jour Theory Probab. Appl.

\yr 1963

\vol 8

\issue 4

\pages 436--439

\crossref{https://doi.org/10.1137/1108049}

Linking options:

https://www.mathnet.ru/eng/tvp4694

https://www.mathnet.ru/eng/tvp/v8/i4/p470

This publication is cited in the following 13 articles:

Introduction to Petroleum Seismology, 2018, 1319
Geoffrey P. Cureton, “Retrieval of Higher Order Ocean Spectral Information From Sunglint”, IEEE Trans. Geosci. Remote Sensing, 53:1 (2015), 36
David R. Brillinger, Selected Works of David Brillinger, 2012, 149
Qing Zhao, Jia Ye, “Quickest Detection in Multiple On–Off Processes”, IEEE Trans. Signal Process., 58:12 (2010), 5994
Introduction to Petroleum Seismology, 2005, 659
B. Picinbono, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99, 1999, 320
Ananthram Swami, Georgios B. Giannakis, Guotong Zhou, “Bibliography on higher-order statistics”, Signal Processing, 60:1 (1997), 65
B. Picinbono, “Ergodicity and fourth-order spectral moments”, IEEE Trans. Inform. Theory, 43:4 (1997), 1273
D.R. Willinger, Workshop on Higher-Order Spectral Analysis, 1989, 41
C.L. Nikias, M.R. Raghuveer, “Bispectrum estimation: A digital signal processing framework”, Proc. IEEE, 75:7 (1987), 869
T. Matsuoka, T.J. Ulrych, “Phase estimation using the bispectrum”, Proc. IEEE, 72:10 (1984), 1403
D.J. Thomson, “Spectrum estimation and harmonic analysis”, Proc. IEEE, 70:9 (1982), 1055
Yu. V. Prohorov, Yu. A. Rozanov, Probability Theory, 1969, 304

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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