Literature cited
I. G. Zhurbenko, “Spectral semiinvariants of stationary processes with sufficiently strong mixing,” Teor. Veroyat. i ee Prim.,17, No. 1 (1972).
N. M. Zuev, “Investigation of the spectral densities of stochastic processes with mixing,” Dokl. Akad. Nauk SSSR,207, No. 4 (1972).
A. N. Shiryaev, “Certain questions of the spectral theory of higher moments,” Teor. Veroyat. i ee Prim.,5, No. 3 (1960).
V. P. Leonov, Some Applications of Higher Semiinvariants to the Theory of Stationary Stochastic Processes [in Russian], Nauka, Moscow (1964).
I. A. Ibragimov, “On an estimate for the spectrum of a stationary Gaussian process,” Dokl. Akad. Nauk SSSR,141, No. 2 (1961).
I. A. Ibragimov, “On an estimate for the spectral function of a stationary Gaussian process,” Teor. Veroyat. i ee Prim.,8, No. 4 (1963).
I. A. Ibragimov and T. M. Tovstik, “On an estimate for the spectral functions of a class of stationary stochastic sequences,” Vestnik LGU, No. 1 (1964).
R. Bentkus, “On the asymptotic behavior of an estimate of the spectral function of a multivariate stationary Gaussian sequence,” Litovskii Matem. Sb.,11, No. 4 (1971).
D. R. Brillinger, “Asymptotic properties of spectral estimates of second order,” Biometrica,56, 375–390 (1969).
E. Parzen, “On consistent estimates of the spectrum of a stationary time series,” Ann. Math. Statistics,28, No. 2, 329–348 (1957).
I. G. Zhurbenko, “On sharp estimates of mixed semiinvariants of stochastic processes,” Sib. Matem. Zh.,13, No. 2 (1972).
V. A. Statulyavichus, “On limit theorems for random functions, I,” Litovskii Matem. Sb.,10, No. 3 (1970).
B. Ryauba, “On the central limit theorem for sums of series of weakly dependent random variables,” Litovskii Matem. Sb.,2, No. 2 (1962).
I. M. Gel'fand and G. E. Shilov, Generalized Functions and Actions on Them [in Russian], Fizmatgiz, Moscow (1959).
I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Connected Variables [in Russian], Nauka, Moscow (1965).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 27, No. 4, pp. 452–463, July–August, 1975.
The authors express their sincere gratitude to A. N. Kolmogorov for his constant interest in the problems discussed here.
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Zhurbenko, I.G., Zuev, N.M. On higher spectral densities of stationary processes with mixing. Ukr Math J 27, 364–373 (1975). https://doi.org/10.1007/BF01085581
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DOI: https://doi.org/10.1007/BF01085581