Article PDF
References
Busacker, R.G., Saaty, T.L.: Finite Graphs and Networks: An Introduction with Applications. New York: McGraw-Hill 1966
Carmona, R., KÔno, N.: Convergence en loi et lois du logarithme itéré pour les vecteurs gaussiens. To appear in Z. Wahrscheinlichkeitstheorie verw. Geb. (1977)
De Haan, L.: On regular variation and its application to the weak convergence of sample extremes. Math. Centre Tracts32, Math. Centre, Amsterdam (1970)
Dobrushin, R.L.: Gaussian and their subordinated automodel random generalized fields. To appear in Ann. Probability (1977)
Edmonds, J., Fulkerson, D.R.: Transversals and matroid partition. J. Res. National Bureau of Standards69B (Math. and Math. Phys.), 147–153 (1965)
Fernique, X.: Continuité des processus gaussians. C.R. Acad. Sc. Paris258, 6058–6059 (1964)
Fisher, M.E.: The renormalization group in the theory of critical behavior. Rev. Modern Phys.46, 597–616 (1974)
Gantmacher, F.R.: The theory of matrices, Vol. 2. New York: Chelsea 1959
Gross, L.: Logarithmic Sobolev inequalities. Amer. J. Math.97, 1061–1083 (1975)
Harary, F.: Graph theory. Reading: Addison-Wesley 1969
Isserlis, L.: On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables. Biometrika12, 134–139 (1919)
Jona-Lasinio, G.: Probabilistic approach to critical phenomena. Preprint n. 32. Instituto di Fisica “G. Marconi.” Università di Roma (1977)
Kibble, W.F.: An extension of a theorem of Mehler's on Hermite polynomials. Proc. Cambridge Philos. Soc.41, 12–15 (1945)
Kolmogorov, A.N.: Wienersche Spiralen und einige andere interessante Kurven in Hilbertschen Raum. C.R. (Doklady) Acad. Sci. URSS (N.S.),26, 115–118 (1940)
Kuelbs, J.: A strong convergence theorem for Banach space valued random variables. Ann. Prob.4, 744–771 (1976)
Ma, S.: Modern Theory of Critical Phenomena. (Frontiers in Physics). Reading: Benjamin 1976
Mandelbrot, B.: Fractals: Form, Chance and Dimension. San Francisco: W.H. Freeman 1977
Mandelbrot, B., Van Ness, J.W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev.10, 422–437 (1968)
Neveu, J.: Mathematical foundations of the calculus of probability. San Francisco: Holden-Day 1965
Oodaira, H.: On Strassen's version of the law of iterated logarithm for Gaussian processes. Z. Wahrscheinlichkeitstheorie verw. Geb.21, 289–299 (1972)
Oodaira, H.: The law of the iterated logarithm for Gaussian processes. Ann. Prob.1, 954–967 (1973a)
Oodaira, H.: The log log law for certain dependent random sequences. Proc. Second Japan-USSR Symp. Prob. Theory. Lecture notes in Math.330, 355–369. Berlin: Springer Verlag (1973b)
Rosenbloom, P.C., Widder, D.V.: Expansions in terms of heat polynomials and associated functions. Trans. Amer. Math. Soc.92, 220–266 (1959)
Serfling, R.J.: Moment inequalities for the maximum cumulative sum. Ann. Math. Stat.41, 1227–1234 (1970)
SinaÏ, Ya.G.: Automodel probability distributions (In Russian). Teor. Veroyatnost. i Ee Primenen.21, 63–80 (1976)
Slepian, D.: On the symmetrized Kronecker power of a matrix and extensions of Mehler's formula for Hermite polynomials. SIAM J. Math. Anal.3, 606–616 (1972)
Taqqu, M.S.: Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie verw. Geb.31, 287–302 (1975)
Wilson, K., Kogut, J.: The renormalization group and the ɛ expansion. Physics reports12C, 75–200 (1974)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/BF00736047
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00736047