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Chow, Y.S., Studden, W.J.: Montonicity of the variance under truncation and variations of Jensen's inequality. Ann. Math. Statist.40, 1106–1108 (1969)
Doob, J.L.: Stochastic processes. New York: Wiley 1953
Egorov, V.A.: On the law of the iterated logarithm. Theor. Probability Appl.14, 693–699 (1969)
Egorov, V.A.: On the strong law of large numbers and the law of the iterated logarithm for sequences of independent random variables. Theor. Probability Appl. 509–514 (1970)
Egorov, V.A.: Some theorems on the strong law of large numbers and the law of the iterated logarithm. Theor. Probability Appl.17, 86–100 (1972)
Egorov, V.A.: Some sufficient conditions for the law of the iterated logarithm. Theor. Probability Math. Statist.3, 61–67 (1974)
Feller, W.: An extension of the law of the iterated logarithm to variables without variance. J. Math. Mech.18, 343–355 (1968)
Fernholz, L.T., Teicher, H.: Stability of random variables and iterated logarithm laws for martingales and quadratic forms. Ann. Probability8, 765–774 (1980)
Kesten, H.: Sums of independent random variables — without moment conditions. Ann. Math. Statist.43, 701–732 (1972)
Klass, M.J.: Toward a universal law of the iterated logarithm, Part I. Z. Wahrscheinlichkeitstheorie verw. Gebiete36, 165–178 (1976)
Klass, M.J.: Toward a universal law of the iterated logarithm, Part II. Z. Wahrscheinlichkeitstheorie verw. Gebiete39, 151–165 (1977)
Klass, M., Teicher, H.: Iterated logarithm laws for asymmetric random variables barely with or without finite mean. Ann. Probability5, 861–874 (1977)
Loève, M.: Probability theory (3rd ed.). Princeton: Van Nostrand 1963
Martikainen, A.I., Petrov, V.V.: On necessary and sufficient conditions of the law of the iterated logarithm. Theor. Probability Appl.22, 16–23 (1977)
Rosenthal, H.P.: On the sequences of Lp(p>2) spanned by sequences of independent random variables. Israel J. Math.8, 273–303 (1970)
Teicher, H.: On the law of the iterated logarithm. Ann. Probability2, 714–728 (1974)
Teicher, H.: A necessary condition for the iterated logarithm law. Z. Wahrscheinlichkeitstheorie verw. Gebiete31, 343–349 (1975)
Teicher, H.: Generalized exponential bounds, iterated logarithm and strong laws. Z. Wahrscheinlichkeitstheorie verw. Gebiete48, 293–307 (1979)
Tomkins, R.J.: Some iterated logarithm results related to the central limit theorem. Trans. Amer. Math. Soc.156, 185–192 (1971)
Tomkins, R.J.: Limit theorems without moment hypotheses for sums of independent random variables. Ann. Probability8, 314–324 (1980)
Tomkins, R.J.: Lindeberg functions and the law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie verw. Gebiete65, 135–143 (1983)
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The work of this author was supported in part by NSF grant #MCS-80-04022
The work of this author was supported by a grant from the Natural Sciences and Engineering Research Council of Canada
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Klass, M.J., Tomkins, R.J. On the limiting behavior of normed sums of independent random variables. Z. Wahrscheinlichkeitstheorie verw Gebiete 68, 107–120 (1984). https://doi.org/10.1007/BF00535177
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DOI: https://doi.org/10.1007/BF00535177