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Teoriya Veroyatnostei i ee Primeneniya, 1960, Volume 5, Issue 2, Pages 222–227 (Mi tvp4828)  

This article is cited in 213 scientific papers (total in 214 papers)

Short Communications

On Strong Mixing Conditions for Stationary Gaussian Processes

A. N. Kolmogorov, Yu. A. Rozanov

Moscow
Abstract: This paper considers conditions, which guarantee strong mixing of stationary random Gaussian process ξ(t).
It is proved, for example, that if the spectral density f(λ) of the process ξ(t) is continuous and positive (parameter t is discrete) or f(λ) is positive and uniformly continuous, and for large λ
mλkf(λ)Mλk1
(parameter t is continuous), then strong mixing takes place.
Received: 18.11.1959
English version:
Theory of Probability and its Applications, 1960, Volume 5, Issue 2, Pages 204–208
DOI: https://doi.org/10.1137/1105018
Document Type: Article
Language: Russian
Citation: A. N. Kolmogorov, Yu. A. Rozanov, “On Strong Mixing Conditions for Stationary Gaussian Processes”, Teor. Veroyatnost. i Primenen., 5:2 (1960), 222–227; Theory Probab. Appl., 5:2 (1960), 204–208
Citation in format AMSBIB
\Bibitem{KolRoz60}
\by A.~N.~Kolmogorov, Yu.~A.~Rozanov
\paper On Strong Mixing Conditions for Stationary Gaussian Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1960
\vol 5
\issue 2
\pages 222--227
\mathnet{http://mi.mathnet.ru/tvp4828}
\transl
\jour Theory Probab. Appl.
\yr 1960
\vol 5
\issue 2
\pages 204--208
\crossref{https://doi.org/10.1137/1105018}
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  • https://www.mathnet.ru/eng/tvp4828
  • https://www.mathnet.ru/eng/tvp/v5/i2/p222
  • This publication is cited in the following 214 articles:
    1. Xiutao Yang, Shanchao Yang, Yufang Li, Dan Liang, “Berry-Esseen bounds of asymptotic normality of kernel density estimator for long-span high-frequency data with α -mixing”, Statistics, 2025, 1  crossref
    2. S. O. Sharipov, “Funktsionalnaya predelnaya teorema dlya kriticheskogo vetvyaschegosya protsessa so slabo zavisimoi immigratsiei”, Diskret. matem., 36:1 (2024), 136–148  mathnet  crossref
    3. Taehyun Kim, Woonyoung Chang, Jeongyoun Ahn, Sungkyu Jung, “Double data piling: a high-dimensional solution for asymptotically perfect multi-category classification”, J. Korean Stat. Soc., 2024  crossref
    4. ZHISHUI HU, IOANNIS KASPARIS, QIYING WANG, “TIME-VARYING PARAMETER REGRESSIONS WITH STATIONARY PERSISTENT DATA”, Econom. Theory, 2024, 1  crossref
    5. Zhao-Ang Zhang, “Strong law of large numbers for linear processes under sublinear expectation”, Communications in Statistics - Theory and Methods, 53:6 (2024), 2205  crossref
    6. Liangxue Li, Xuejun Wang, Chen Yi, “Complete f -moment convergence for a class of random variables with related statistical applications”, Stochastic Models, 40:2 (2024), 375  crossref
    7. Dagmara Dudek, Anna Kuczmaszewska, “Some practical and theoretical issues related to the quantile estimators”, Stat Papers, 2024  crossref
    8. Emily T. Winn-Nuñez, Maryclare Griffin, Lorin Crawford, “A simple approach for local and global variable importance in nonlinear regression models”, Computational Statistics & Data Analysis, 194 (2024), 107914  crossref
    9. Shunping Zheng, Fei Zhang, Yan Shen, Xuejun Wang, Jinxiang Ou, “Convergence properties for randomly weighted sums of ρ -mixing sequences with related statistical applications”, Communications in Statistics - Simulation and Computation, 2024, 1  crossref
    10. Shanchao Yang, Lanjiao Qin, Y. Wang, X. Yang, “Asymptotic normality of kernel density estimation for mixing high-frequency data”, Journal of Nonparametric Statistics, 2024, 1  crossref
    11. Yi Wu, Xuejun Wang, “On Berry–Esséen bound of frequency polygon estimation under ρ-mixing samples”, Metrika, 2024  crossref
    12. Rahul Biswas, Somabha Mukherjee, “Consistent causal inference from time series with PC algorithm and its time-aware extension”, Stat Comput, 34:1 (2024)  crossref
    13. Shanchao Yang, Yanzhe Wang, Lanjiao Qin, Xin Yang, “Asymptotic normality of Nadaraya–Waton kernel regression estimation for mixing high-frequency data”, Statistics, 58:1 (2024), 87  crossref
    14. Hajo Holzmann, Bernhard Klar, “Lancaster correlation: A new dependence measure linked to maximum correlation”, Scandinavian J Statistics, 2024  crossref
    15. Richard C. Bradley, “ON SOME POSSIBLE COMBINATIONS OF MIXING RATES FOR STRICTLY STATIONARY, REVERSIBLE MARKOV CHAINS”, Rocky Mountain J. Math., 54:2 (2024)  crossref
    16. Hao Chen, Abhishek Gupta, Yin Sun, Ness Shroff, “Model-Free Change Point Detection for Mixing Processes”, IEEE Open J. Control. Syst., 3 (2024), 202  crossref
    17. Thomas Mikosch, Olivier Wintenberger, Springer Series in Operations Research and Financial Engineering, Extreme Value Theory for Time Series, 2024, 161  crossref
    18. R. Maya, M. R. Irshad, Christophe Chesneau, Francesco Buono, Maria Longobardi, Flexible Nonparametric Curve Estimation, 2024, 95  crossref
    19. Dan Liang, Shanchao Yang, “Asymptotic properties of recursive kernel density estimation for long-span high-frequency data”, Communications in Statistics - Theory and Methods, 2024, 1  crossref
    20. P. A. Yaskov, “Spontaneously started signals with white noise”, Theory Probab. Appl., 69:4 (2025), 565–578  mathnet  crossref  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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