Lai, Tze Leung; Stout, William Limit theorems for sums of dependent random variables. (English) Zbl 0419.60026 Z. Wahrscheinlichkeitstheor. Verw. Geb. 51, 1-14 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 15 Documents MSC: 60F15 Strong limit theorems 60E15 Inequalities; stochastic orderings Keywords:law of the iterated logarithm; strongly dependent stationary Gaussian random variables; Marcinkiewicz-Zygmund type strong law Citations:Zbl 0272.60013; Zbl 0302.60018 PDFBibTeX XMLCite \textit{T. L. Lai} and \textit{W. Stout}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 51, 1--14 (1980; Zbl 0419.60026) Full Text: DOI References: [1] Azuma, K.: Weighted sums of certain dependent random variables. T?hoku Math. J. 19, 357-367 (1967) · Zbl 0178.21103 [2] Dharmadhikari, S.W., Jogdeo, K.: Bounds on moments of sums of random variables. Ann. Math. Statist. 40, 1506-1509 (1969) · Zbl 0208.44903 [3] Esseen, C.G., von Bahr, B.: Inequalities for the r th absolute moment of a sum of random variables, 1?r?2. Ann. Math. Statist. 36, 299-303 (1965) · Zbl 0134.36902 [4] Feller, W.: One-sided analogues of Karamata’s regular variation. L’Enseignement Math. 15, 107-121 (1969) · Zbl 0177.08201 [5] G?l, I.S.: Sur la majoration des suites de fonctions. Proc. Koninkl. Nederl. Akad. Wetensch. Ser. A 54, 243-251 (1951) · Zbl 0044.06901 [6] Hartman, P., Wintner, A.: On the law of the iterated logarithm. Amer. J. Math. 63, 169-176 (1941) · JFM 67.0460.03 [7] Lai, T.L., Stout, W.: The law of the iterated logarithm and upper-lower class tests for partial sums of stationary Gaussian sequences. Ann. Probability 6, 731-750 (1978) · Zbl 0403.60032 [8] Longnecker, M., Serfling, R.J.: General moment and probability inequalities for the maximum partial sum. Acta Math. Acad. Scient. Hungar. 30, 129-133 (1977) · Zbl 0373.60066 [9] Philipp, W.: Das Gesetz vom iterierten Logarithmus f?r stark mischende station?re Prozesse. Z. Wahrscheinlichkeitstheorie verw. Gebiete 8, 204-209 (1967) · Zbl 0178.19602 [10] Philipp, W., Stout, W.: Almost sure invariance principles for sums of weakly dependent random variables. Mem. Amer. Math. Soc. No. 161. Providence, R.I.: Amer. Math. Soc. 1975 · Zbl 0361.60007 [11] Rademacher, H.: Einige S?tze ?ber Reihen von allgemeinen Orthogonalfunktionen. Math. Ann. 87, 112-138 (1922) · JFM 48.0485.05 [12] Rosenblatt, M.: Independence and dependence. Proc. Fourth Berkeley Sympos. Math. Statist. Probability Univ. Calif. 2, 431-443 (1961) · Zbl 0105.11802 [13] Serfling, R.J.: Moment inequalities for maximum cumalative sum. Ann. Math. Statist. 41, 1227-1234 (1970) · Zbl 0272.60013 [14] Serfling, R.J.: Convergence properties of S n under moment restrictions. Ann. Math. Statist. 41, 1235-1248 (1970) · Zbl 0302.60018 [15] Stout, W.: Maximal inequalities and the law of the iterated logarithm. Ann. Probability 1, 322-328 (1973) · Zbl 0262.60016 [16] Takahashi, S.: Notes on the law of the iterated logarithm. Studia Sci. Math. Hungar. 7, 21-24 (1972) · Zbl 0325.60030 [17] Taqqu, M.S.: Law of the iterated logarithm for sums of nonlinear functions of Gaussian variables that exhibit a long range dependence. Z. Wahrscheinlichkeitstheorie verw. Gebiete 40, 203-238 (1977) · Zbl 0358.60048 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.