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Literature Cited
R. Bentkus and R. Rudzkis, “Exponential estimates of the distribution of random variables,” Liet. Mat. Rinkinys,20, No. 1, 15–30 (1980).
P. Breuer and P. Major, “Central limit theorems for nonlinear functionals of Gaussian fields,” J. Multivar. Anal.,13, 425–441 (1983).
R. L. Dobrushin and P. Major, “Noncentral limit theorems for nonlinear functionals of Gaussian fields,” Z. Wahr. Verw. Geb.,50, 27–52 (1979).
L. Giraitis and D. Surgailis, “CLT and other limit theorems for functionals of Gaussian processes” (to appear).
L. Giraitis, “Limit theorems for local functionals,” in: Abstracts of the 24th Lithuanian Mathematical Society [in Russian], Vilnius (1983), pp. 52, 53.
V. V. Gorodetskii, “Invariance principle for functions of stationary related Gaussian variables,” J. Sov. Math.,24, No. 5 (1984).
I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Related Variables [in Russian], Nauka, Moscow (1965).
V. A. Malyshev, “Cluster expansions in lattice models of the statistical physics of quantum field theory,” Usp. Mat. Nauk,35, No. 2, 3–51 (1980).
S. G. Krein (ed.), Functional Analysis. Mathematical Bibliographical Handbook [in Russian], Nauka, Moscow (1972).
A. Plikusas, “Multiple Ito integrals,” Liet. Mat. Rinkinys,21, No. 2, 163–173 (1981).
M. Rosenblatt, “Independence and dependence,” in: Proc. Fourth Berkeley Symp. Math. Statist. Probab., Berkeley (1961), pp. 431–443.
J. Shohat, “The relation of the classical orthogonal polynomials to the polynomials of Appell,” Am. J. Math.,58, 453–464 (1936).
T. C. Sun, “Some further results on central limit theorems for nonlinear functions of normal stationary process,” J. Math. Mech.,14, 71–85 (1965).
D. Surgailis, “On Poisson multiple stochastic integrals and associated equilibrium Markov processes,” in: Lect. Notes Contr. Inf. Sciences, Vol. 49, Springer-Verlag (1983), pp. 233–248.
D. Surgailis, “Zones of attraction of self-similar multiple integrals,” Liet. Mat. Rinkinys,22, No. 3, 185–201 (1982).
M. S. Taqqu, “Weak convergence to fractional Brownian motion and to the Rosenblatt process,” Z. Wahr. Verw. Geb.,31, 287–302 (1975).
M. S. Taqqu, “Convergence of iterated processes of arbitrary Hermite rank”, Z. Wahr. Verw. Geb.,50, 53–83 (1979).
C. S. Withers, “Central limit theorems for dependent variables. I,” Z. Wahr. Verw. Geb.,57, No. 4, 509–535 (1981).
L. Giraitis, “Convergence of certain nonlinear transformations of a Gaussian sequence to self-similar processes,” Liet. Mat. Rinkinys,23, No. 1, 57–68 (1983).
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Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 25, No. 1, pp. 43–57, January–March, 1985.
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Giraitis, L. Central limit theorem for functionals of a linear process. Lith Math J 25, 25–35 (1985). https://doi.org/10.1007/BF00966294
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DOI: https://doi.org/10.1007/BF00966294