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Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 1, Pages 24–37 (Mi tvp1547)  

This article is cited in 14 scientific papers (total in 15 papers)

On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition. II. Sufficient conditions. Mixing rate

I. A. Ibragimov

Leningrad
Abstract: This paper is a continuation of [1] . The theorems of §4 give some criteria for the strong mixing condition. §5 contains the complete description of stationary Gaussian processes with power or exponential decrease rate of α(n).
Received: 05.10.1968
English version:
Theory of Probability and its Applications, 1970, Volume 15, Issue 1, Pages 23–36
DOI: https://doi.org/10.1137/1115002
Bibliographic databases:
Language: Russian
Citation: I. A. Ibragimov, “On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition. II. Sufficient conditions. Mixing rate”, Teor. Veroyatnost. i Primenen., 15:1 (1970), 24–37; Theory Probab. Appl., 15:1 (1970), 23–36
Citation in format AMSBIB
\Bibitem{Ibr70}
\by I.~A.~Ibragimov
\paper On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition. II.~Sufficient conditions. Mixing rate
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 1
\pages 24--37
\mathnet{http://mi.mathnet.ru/tvp1547}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=268951}
\zmath{https://zbmath.org/?q=an:0214.16402|0213.19504}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 1
\pages 23--36
\crossref{https://doi.org/10.1137/1115002}
Linking options:
  • https://www.mathnet.ru/eng/tvp1547
  • https://www.mathnet.ru/eng/tvp/v15/i1/p24
  • This publication is cited in the following 15 articles:
    1. A. A. Borovkov, Al. V. Bulinski, A. M. Vershik, D. Zaporozhets, A. S. Holevo, A. N. Shiryaev, “Ildar Abdullovich Ibragimov (on his ninetieth birthday)”, Russian Math. Surveys, 78:3 (2023), 573–583  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Shanchao Yang, Jiaying Xie, Shuyi Luo, Zhiyong Li, Xin Yang, “Moment inequalities for mixing long-span high-frequency data and strongly consistent estimation of OU integrated diffusion process”, J Inequal Appl, 2023:1 (2023)  crossref
    3. Raymond Cheng, Charles B. Harris, “Mixed‐Norm Spaces and Prediction of SαS Moving Averages”, Journal Time Series Analysis, 36:6 (2015), 853  crossref
    4. Mikosch T. Wintenberger O., “Precise Large Deviations for Dependent Regularly Varying Sequences”, Probab. Theory Relat. Field, 156:3-4 (2013), 851–887  crossref  isi
    5. Richard C. Bradley, “On the behavior of the covariance matrices in a multivariate central limit theorem under some mixing conditions”, Illinois J. Math., 56:3 (2012)  crossref
    6. Violetta Dalla, Javier Hidalgo, “A parametric bootstrap test for cycles”, Journal of Econometrics, 129:1-2 (2005), 219  crossref
    7. Richard C. Bradley, “A criterion for a continuous spectral density”, Journal of Multivariate Analysis, 86:1 (2003), 108  crossref
    8. R Cheng, “Rational spectral densities and strong mixing”, Journal of Multivariate Analysis, 42:2 (1992), 267  crossref
    9. Y.S. Rama Krishnaiah, “On the Glivenko–Cantelli theorem for generalized empirical processes based on strong mixing sequences”, Statistics & Probability Letters, 10:5 (1990), 439  crossref
    10. P. M. Robinson, “On the consistency and finite-sample properties of nonparametric kernel time series regression, autoregression and density estimators”, Ann Inst Stat Math, 38:3 (1986), 539  crossref
    11. Radhey S. Singh, Aman Ullah, “Nonparametric Time-Series Estimation of Joint DGP, Conditional DGP, and Vector Autoregression”, Econ Theory, 1:1 (1985), 27  crossref
    12. F. Götze, C. Hipp, “Asymptotic expansions for sums of weakly dependent random vectors”, Z. Wahrscheinlichkeitstheorie verw Gebiete, 64:2 (1983), 211  crossref
    13. P. M. Robinson, “NONPARAMETRIC ESTIMATORS FOR TIME SERIES”, Journal Time Series Analysis, 4:3 (1983), 185  crossref
    14. V. V. Peller, S. V. Khrushchev, “Hankel operators, best approximations, and stationary Gaussian processes”, Russian Math. Surveys, 37:1 (1982), 61–144  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. Yosihiko Ogata, “Maximum likelihood estimates of incorrect Markov models for time series and the derivation of AIC”, Journal of Applied Probability, 17:1 (1980), 59  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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