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Non-central limit theorems for non-linear functionals of Gaussian fields. (English) Zbl 0397.60034


MSC:

60F99 Limit theorems in probability theory
60G15 Gaussian processes
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[1] Dobrushin, R. L., Gaussian and their subordinated self-similar random fields, Ann. Probability, 7, No. 1, 1-28 (1979) · Zbl 0392.60039
[2] Dobrushin, R. L., Automodel generalized random fields and their renorm group, Multi-component stochastic systems (in Russian), 179-213 (1978), Moscow: Nauka, Moscow
[3] Dobrushin, R. L.; Minlos, R. A., Polynomials of random functions. (in Russian) Achievements, Uspeschi, Math. Sci. XXXII. No 2, 194, 67-122 (1977) · Zbl 0364.60055
[4] Dobrushin, R.L., Takahashi, J.: Self-similar Gaussian fields. [To appear]
[5] Ibragimov, I. A.; Linnik, J. V., Independent and stationary sequences of random variables (1971), Groningen: Walters-Noordhoff, Groningen · Zbl 0219.60027
[6] Rosenblatt, M.,: Independence and dependence. Proc. 4th Sympos. Math. Statist. Probability pp. 411-443. Univ. California: Berkeley University Press 1961 · Zbl 0105.11802
[7] Simon, B., The P(φ)_2Euclidean (Quantum) field theory (1974), Princeton: Princeton University Press, Princeton · Zbl 1175.81146
[8] Taqqu, M. S., Weak convergence to Fractional Brownian Motion and the Rosenblatt Process, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 31, 287-302 (1975) · Zbl 0303.60033
[9] Zygmund, A., Trigonometric series (1959), Cambridge: Cambridge University Press, Cambridge · JFM 58.0280.01
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