On the limit distribution of the correlogram of a stationary Gaussian process with weak decrease in correlation
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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.
KeywordsCorrelation Function Spectral Density Statistical Estimate Gaussian Process Limit Distribution
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- 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).Google Scholar
- 7.N. Terrin and M. S. Taqqu,A Concentral Limit Theorem for Quadratic Forms of Gaussian Stationary Sequences, Preprint, Boston (1989).Google Scholar
- 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).Google Scholar
- 11.W. FeiLer,An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley, New York (1966).Google Scholar