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Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables. (English) Zbl 0388.60048


MSC:

60G50 Sums of independent random variables; random walks
60F99 Limit theorems in probability theory
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[1] Dobrushin, R. L., Gaussian and their subordinated self-similar random generalized fields, Ann. Probability, 7, 1-28 (1979) · Zbl 0392.60039
[2] Ibragimov, I. A.; Linnik, Yu. V., Independent and Stationary Sequences of Random Variables (1971), Gröningen: Walters-Noordhoff, Gröningen · Zbl 0219.60027
[3] Rosenblatt, M.: Independence and dependence. Proc. 4th Berkeley Sympos. Math. Statist. Probab., 431-443. Univ. Calif. (1961) · Zbl 0105.11802
[4] Rosenblatt, M., Fractional integrals of stationary processes and the central limit theorem, J. Appl. Probability, 13, 723-732 (1976) · Zbl 0354.60010
[5] Sun, T. C., Some further results on central limit theorems for non-linear functions of a normal stationary process, J. Math. Mech., 14, 71-85 (1965) · Zbl 0138.10803
[6] Taqqu, M. S., Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 31, 287-302 (1975) · Zbl 0303.60033
[7] Taqqu, M. S., Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence. Z. Wahrscheinlichkeitstheorie verw, Gebiete, 40, 203-238 (1977) · Zbl 0358.60048
[8] Taqqu, M.S.: A representation for self-similar processes, manuscript · Zbl 0373.60048
[9] Zygmund, A., Trigonometric Series (1968), Cambridge: Cambridge University Press, Cambridge · JFM 58.0280.01
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