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December, 1979 Extension of the Darling and Erdos Theorem on the Maximum of Normalized Sums
Galen R. Shorack
Ann. Probab. 7(6): 1092-1096 (December, 1979). DOI: 10.1214/aop/1176994906

Abstract

The limiting distribution of $\max_{1\leqslant k \leqslant n}S_k/k^{\frac{1}{2}}$ is derived via embedding. The theorem also applies to partial sums of certain dependent rv's. Thus the proof of the Darling and Erdos result is brought into line with recent literature; moreover, the scope of its applicability is greatly increased in regard both to dependence and moment assumptions.

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Galen R. Shorack. "Extension of the Darling and Erdos Theorem on the Maximum of Normalized Sums." Ann. Probab. 7 (6) 1092 - 1096, December, 1979. https://doi.org/10.1214/aop/1176994906

Information

Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0421.60046
MathSciNet: MR548907
Digital Object Identifier: 10.1214/aop/1176994906

Subjects:
Primary: 60G50
Secondary: 60B10 , 60F05

Keywords: dependent rv's , ‎embedding‎ , extreme value distribution , Maximum of normalized sums , normalized Brownian motion , Uhlenbeck process

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 6 • December, 1979
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