×

Convergence of integrated processes of arbitrary Hermite rank. (English) Zbl 0397.60028


MSC:

60F05 Central limit and other weak theorems
60G99 Stochastic processes
82B26 Phase transitions (general) in equilibrium statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Davydov, Yu. A., The invariance principle for stationary processes, Theor. Probability Appl., 15, 487-498 (1970) · Zbl 0219.60030
[2] DeHaan, L., On regular variation and its application to the weak convergence of sample extremes, Math. Centre Tracts 32 (1970), Amsterdam: Math. Centre, Amsterdam · Zbl 0226.60039
[3] Dobrushin, R. L., Gaussian and their subordinated self-similar random generalized fields, Ann. Probability, 7, 1-28 (1979) · Zbl 0392.60039
[4] Dobrushin, R. L.; Major, P., Non-central limit theorems for non-linear functionals of Gaussian fields, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 50, 27-52 (1979) · Zbl 0397.60034
[5] Itô, K., Multiple Wiener integral, J. Math. Soc. Japan, 3, 157-164 (1951) · Zbl 0044.12202
[6] Jona-Lasinio, G.; Lévy, M.; Mitter, P., Probabilistic approach to critical behavior, New Developments in Quantum Field Theory and Statistical Mechanics, Cargese 1976, 419-446 (1977), New York: Plenum, New York
[7] Lawrance, A. J.; Kottegoda, N. T., Stochastic modelling of riverflow time series, J. Royal Statist. Soc. Ser. A, 140, 1-47 (1977)
[8] McKean, H. P., Geometry of differential space, Ann. Probability, 1, 197-206 (1973) · Zbl 0263.60035
[9] Mandelbrot, B.; Van Ness, J. W., Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10, 422-437 (1968) · Zbl 0179.47801
[10] Sinaï, Ya. G., Self-similar probability distributions, Theor. Probability Appl., 21, 64-80 (1976) · Zbl 0358.60031
[11] 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
[12] 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
[13] Taqqu, M. S., A representation for self-similar processes, Stochastic Processes Appl., 7, 55-64 (1978) · Zbl 0373.60048
[14] Taqqu, M.S.: Weak convergence at all Hermite ranks. Techn. Report No. 389, August 3, 1978. School of Operations Research, Cornell University (1978b)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.