Annals of Probability

Some Comments on the Erdos-Renyi Law and a Theorem of Shepp

James Lynch

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Abstract

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.

Article information

Source
Ann. Probab., Volume 11, Number 3 (1983), 801-802.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993526

Digital Object Identifier
doi:10.1214/aop/1176993526

Mathematical Reviews number (MathSciNet)
MR704565

Zentralblatt MATH identifier
0518.60037

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60F10: Large deviations

Keywords
Strong laws moving averages large deviations

Citation

Lynch, James. Some Comments on the Erdos-Renyi Law and a Theorem of Shepp. Ann. Probab. 11 (1983), no. 3, 801--802. doi:10.1214/aop/1176993526. https://projecteuclid.org/euclid.aop/1176993526


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