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Major, Peter

Limit theorems for non-linear functionals of Gaussian sequence. (English) Zbl 0444.60028

Z. Wahrscheinlichkeitstheor. Verw. Geb. 57, 129-158 (1981).
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Cited in 24 Documents

MSC:

60F17 Functional limit theorems; invariance principles

Keywords:

non-linear functionals of Gaussian sequences

Citations:

Zbl 0397.60034; Zbl 0388.60048
PDFBibTeX XMLCite
\textit{P. Major}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 57, 129--158 (1981; Zbl 0444.60028)
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References:

[1] Dobrushin, R. L., Gaussian and their subordinated self similar random generalized fields, Ann. Probab., 7, 1-28 (1979) · Zbl 0392.60039
[2] Dobrushin, R. L., Automodel generalized random fields and their renorm group, multicomponent Random Systems (1980), New York: Dekker, New York · Zbl 0499.60047
[3] Dobrushin, R. L.; Major, P., Non-central limit theorems for non-linear functional of Gaussian fields, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 50, 27-52 (1979) · Zbl 0397.60034
[4] Feller, W., An introduction to Probability Theory and its Applications 2 (1971), New York: Wiley, New York · Zbl 0219.60003
[5] Itô, K., Multiple Wiener Integral, J. Math. Soc. Japan, 3, 157-169 (1951) · Zbl 0044.12202
[6] Rosenblatt, M., Independence and dependence, Proc. 4th Berkeley Sympos. Math. Statist Probab, 411-443 (1961), Berkeley: Univ. Calif. Press, Berkeley · Zbl 0105.11802
[7] Rosenblatt, M., Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 49, 125-132 (1979) · Zbl 0388.60048
[8] 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
[9] Taqqu, M. S., A representation for self-similar processes, Stochastic Proc. and their Appl., 7, 55-64 (1978) · Zbl 0373.60048
[10] Taqqu, M. S., Convergence of integrated processes of arbitrary Hermite rank, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 50, 53-83 (1979) · Zbl 0397.60028
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