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A relation between Chung’s and Strassen’s laws of the iterated logarithm. (English) Zbl 0441.60027

60F15 Strong limit theorems
60J65 Brownian motion
Full Text: DOI
[1] Anderson, T.W.: The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6, 170-176 (1955) · Zbl 0066.37402
[2] Bolthausen, E.: On the speed of convergence in Strassen’s law of the iterated logarithm. Ann. Probability 6, 668-672 (1978) · Zbl 0391.60036
[3] Cameron, R.H., Martin, W.T.: Transformation of Wiener integrals under translation. Ann. of Math. 45, 386-396 (1944) · Zbl 0063.00696
[4] Chung, K.L.: On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc. 64, 205-233 (1948) · Zbl 0032.17102
[5] Feller, W.: An introduction to probability theory and its applications. Vol. 2. New York: Wiley 1966 · Zbl 0138.10207
[6] Skorokhod, A.V.: Random processes with independent increments. (Russian). Moscow: Izdat. Nauka 1964
[7] Strassen, V.: An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie verw. Gebiete 3, 211-226 (1964) · Zbl 0132.12903
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