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On the limit distribution of the correlogram of a stationary Gaussian process with weak decrease in correlation

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Abstract

An example of the non-Gaussian limit distribution of the statistical estimate of the correlation function of a stationary Gaussian process with unbounded spectral density (or with a nonintegrable correlation function) is given.

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References

  1. A. V. Ivanov and N. N. Leonenko,Statistical Analysis of Random Fields, Kluwer, Dordrecht-Boston-London (1989).

    Google Scholar 

  2. V. V. Buldygin and V. V. Zayats, “Strong consistency and asymptotic normality of correlation function estimates in different functional spaces,” in:VI USSR-Japan Symposium on Probability Theory and Mathematical Statistics. Abstracts and Communications, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991), p. 30.

    Google Scholar 

  3. M. Rosenblatt, “Some limit theorems for partial sums of quadratic form in stationary Gaussian variables,”Z Wahrscheinlichkeitstheor. Verw. Geb.,49, No. 2, 125–132 (1979).

    Google Scholar 

  4. R. L. Dobrushin and P. Major, “Non-central limit theorems for non-linear functionals of Gaussian fields,”Z. Wahrscheinlichkeits- theor. Verw. Geb.,50, No. 1, 27–52 (1979).

    Google Scholar 

  5. M. S. Taqqu, “Convergence of integral processes of arbitrary Hermite ring,”Z. Wahrscheinlichkeitstheor. Verw. Geb.,50, No. 1, 53–83 (1979).

    Google Scholar 

  6. N. Terrin and M. S. Taqqu,Convergence in Distribution of Sums of Bivariate Appell Polynomials with Long Range Dependence, Preprint, Boston (1989).

  7. N. Terrin and M. S. Taqqu,A Concentral Limit Theorem for Quadratic Forms of Gaussian Stationary Sequences, Preprint, Boston (1989).

  8. M. I. Yadrenko,Spectral Theory of Random Fields [in Russian], Vyshcha Shkola, Kiev (1980).

    Google Scholar 

  9. N. N. Leonenko and A. Ya. Olenko, “The Tauber and Abel theorems for the correlation function of a homogeneous isotropic random field,”Ukr. Mat. Zh.,43, No. 12, 1652–1664 (1991).

    Google Scholar 

  10. A. Ya. Olenko,Some Problems in the Correlation-Spectral Theory of Random Fields [in Russian], Author's Candidates Degree Thesis (Physics and Mathematics), Kiev (1991).

  11. W. FeiLer,An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York (1966).

    Google Scholar 

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Authors and Affiliations

  1. Kiev University, Kiev

    N. N. Leonenko & A. Yu. Portnova

Authors
  1. N. N. Leonenko
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  2. A. Yu. Portnova
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1635–1641, December, 1993.

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Leonenko, N.N., Portnova, A.Y. On the limit distribution of the correlogram of a stationary Gaussian process with weak decrease in correlation. Ukr Math J 45, 1841–1848 (1993). https://doi.org/10.1007/BF01061354

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  • DOI: https://doi.org/10.1007/BF01061354

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