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Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1841–1848 | Cite as

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

  • N. N. Leonenko
  • A. Yu. Portnova
Article

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.

Keywords

Correlation Function Spectral Density Statistical Estimate Gaussian Process Limit Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. V. Ivanov and N. N. Leonenko,Statistical Analysis of Random Fields, Kluwer, Dordrecht-Boston-London (1989).Google Scholar
  2. 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. 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. 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. 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. 6.
    N. Terrin and M. S. Taqqu,Convergence in Distribution of Sums of Bivariate Appell Polynomials with Long Range Dependence, Preprint, Boston (1989).Google Scholar
  7. 7.
    N. Terrin and M. S. Taqqu,A Concentral Limit Theorem for Quadratic Forms of Gaussian Stationary Sequences, Preprint, Boston (1989).Google Scholar
  8. 8.
    M. I. Yadrenko,Spectral Theory of Random Fields [in Russian], Vyshcha Shkola, Kiev (1980).Google Scholar
  9. 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. 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).Google Scholar
  11. 11.
    W. FeiLer,An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York (1966).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • N. N. Leonenko
    • 1
  • A. Yu. Portnova
    • 1
  1. 1.Kiev UniversityKiev

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