Ya. G. Sinai, “On Higher Order Spectral Measures of Ergodic Stationary Processes”, Teor. Veroyatnost. i Primenen., 8:4 (1963), 463–470; Theory Probab. Appl., 8:4 (1963), 429

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Teoriya Veroyatnostei i ee Primeneniya, 1963, Volume 8, Issue 4, Pages 463–470 (Mi tvp4693)

This article is cited in 13 scientific papers (total in 14 papers)

Short Communications

On Higher Order Spectral Measures of Ergodic Stationary Processes

Ya. G. Sinai

Moscow

Full-text PDF (947 kB) Citations (14)

Abstract: In this paper some necessary conditions for the ergodicity of stationary processes belonging to the Fortet class [4] are given in terms of higher order spectral moments. These conditions lead to some new ergodic theorems for such processes and to the fact that certain spectral measures uniquely determine the corresponding processes.

Received: 26.05.1962

English version:
Theory of Probability and its Applications, 1963, Volume 8, Issue 4, Pages 429–436
DOI: https://doi.org/10.1137/1108048

Document Type: Article

Language: Russian

Citation: Ya. G. Sinai, “On Higher Order Spectral Measures of Ergodic Stationary Processes”, Teor. Veroyatnost. i Primenen., 8:4 (1963), 463–470; Theory Probab. Appl., 8:4 (1963), 429–436

Citation in format AMSBIB

\Bibitem{Sin63}

\by Ya.~G.~Sinai

\paper On Higher Order Spectral Measures of Ergodic Stationary Processes

\jour Teor. Veroyatnost. i Primenen.

\yr 1963

\vol 8

\issue 4

\pages 463--470

\mathnet{http://mi.mathnet.ru/tvp4693}

\transl

\jour Theory Probab. Appl.

\yr 1963

\vol 8

\issue 4

\pages 429--436

\crossref{https://doi.org/10.1137/1108048}

Linking options:

https://www.mathnet.ru/eng/tvp4693

https://www.mathnet.ru/eng/tvp/v8/i4/p463

This publication is cited in the following 14 articles:

Élise Janvresse, Emmanuel Roy, Thierry De La Rue, Encyclopedia of Complexity and Systems Science Series, Ergodic Theory, 2023, 217
Élise Janvresse, Emmanuel Roy, Thierry De La Rue, Encyclopedia of Complexity and Systems Science, 2020, 1
David R. Brillinger, Selected Works of David Brillinger, 2012, 465
David R. Brillinger, Selected Works of David Brillinger, 2012, 149
B. Picinbono, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99, 1999, 320
B. Picinbono, “Ergodicity and fourth-order spectral moments”, IEEE Trans. Inform. Theory, 43:4 (1997), 1273
Ananthram Swami, Georgios B. Giannakis, Guotong Zhou, “Bibliography on higher-order statistics”, Signal Processing, 60:1 (1997), 65
S. P. Novikov, L. A. Bunimovich, A. M. Vershik, B. M. Gurevich, E. I. Dinaburg, G. A. Margulis, V. I. Oseledets, S. A. Pirogov, K. M. Khanin, N. N. Chentsova, “Yakov Grigor'evich Sinai (on his sixtieth birthday)”, Russian Math. Surveys, 51:4 (1996), 765–778
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
Mysore R. Raghuveer, Chrysostomos L. Nikias, “Bispectrum estimation via AR modeling”, Signal Processing, 10:1 (1986), 35
T. Matsuoka, T.J. Ulrych, “Phase estimation using the bispectrum”, Proc. IEEE, 72:10 (1984), 1403
D.R. Brillinger, “The identification of polynomial systems by means of higher order spectra”, Journal of Sound and Vibration, 12:3 (1970), 301
M. Rosenblatt, “Remarks on the Burgers Equation”, Journal of Mathematical Physics, 9:7 (1968), 1129

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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