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August, 1983 Some Comments on the Erdos-Renyi Law and a Theorem of Shepp
James Lynch
Ann. Probab. 11(3): 801-802 (August, 1983). DOI: 10.1214/aop/1176993526


We show that the finiteness of the moment generating function is necessary for the finiteness of the lim sup of the moving averages considered by Shepp (1964). This also implies that the same must be true for the Erdos-Renyi law of large numbers.


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James Lynch. "Some Comments on the Erdos-Renyi Law and a Theorem of Shepp." Ann. Probab. 11 (3) 801 - 802, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0518.60037
MathSciNet: MR704565
Digital Object Identifier: 10.1214/aop/1176993526

Primary: 60F15
Secondary: 60F10

Keywords: large deviations , moving averages , strong laws

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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