Literature Cited
A. N. Shiryaev, “Spectral theory of higher moments. I,” Teor. Veroyatn. Primen.,5, No. 3, 293–313 (1960).
D. Brillinger, Time Series: Data Processing and Theory [Russian translation], Mir, Moscow (1980).
V. P. Leonov, Applications of Higher Cumulants to the Theory of Stationary Stochastic Processes [in Russian], Nauka, Moscow (1964).
R. Bentkus, “Cumulants of sesquilinear forms of a stationary sequence,” Liet. Mat. Rinkinys,17, No. 1, 27–46 (1977).
L. Giraitis, “Central limit theorem for functionals of a linear process,” Liet. Mat. Rinkinys,25, No. 1, 43–57 (1985).
F. Avram and M. S. Taqqu, “Generalized powers of strongly dependent random variables,” Ann. Probab.,15,No. 2, 767–775 (1987).
L. Giraitis and D. Surgailis, “Multivariate Appel polynomials and central limit theorem,” in: E. Eberlein and M. S. Taqqu (eds.), Dependence in Probability and Statistics, Birkhäuser, Boston (1986), pp. 21–71.
D. Surgailis, “On Poisson multiple stochastic integrals and associated equilibrium Markov processes,” Lect. Notes Control. Inf. Sci.,49, 233–248 (1983).
V. M. Leonov and A. N. Shiryaev, “Techniques for calculating cumulants,” Teor. Veroyatn. Primen.,4, No. 3, 342–355 (1959).
V. A. Malyshev and R. A. Minlos, Gibbsian Random Fields [in Russian], Nauka, Moscow (1985).
R. Bentkus, “Asymptotic normality of an estimate of a spectral function,” Liet. Mat. Rinkinys,12, No. 3,3–18 (1972).
P. Major, “Multiple Wiener-Ito integrals,” Lect.Notes Math.,849 (1981).
L. Giraitis and D. Surgailis, “CLT and other limit theorems for functionals of Gaussian processes,” Z. Wahr. Verw. Geb.,70, 191–212 (1985).
A. Plikusas, “Multiple Ito integrals,” Liet. Mat. Rinkinys,21, No. 2, 163–173 (1981).
R. Fox and M. Taqqu, “Central limit theorems in random variables having long-range dependence,” Prob. Theor. Related Fields,74, 213–240 (1987).
F. Avram, “Asymptotic sums with dependent indices and convergence to the Gaussian distribution,” Preprint (1988).
F. Avram, “On bilinear forms in Gaussian random variables and Toeplitz matrices,” Prob. Theory Rel. Fields,79, 37–45 (1988).
I. A. Ibragimov, “Estimate of the spectral function of a stationary Gaussian process,” Teor. Veroyatn. Primen.,8, No. 4, 391–430 (1963).
L. Giraitis and D. Surgailis, “Asymptotic normality of the Wittla estimate for processes with long-range dependence,” Trudy Mat. Inst. im. V. A. Steklova (1988).
Additional information
Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 29, No. 2, pp. 266–289, April–June, 1989.
Rights and permissions
About this article
Cite this article
Giraitis, L. Central limit theorem for polynomial forms. I. Lith Math J 29, 109–128 (1989). https://doi.org/10.1007/BF00966074
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00966074