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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Inequalities for $ \max\vert S_k\vert/b_k$ where $ k \in N^r$


Authors: Galen R. Shorack and R. T. Smythe
Journal: Proc. Amer. Math. Soc. 54 (1976), 331-336
MSC: Primary 60G45; Secondary 60G50, 60B10
MathSciNet review: 0400386
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Abstract: Lemma $ 1$ presents a powerful general inequality for $ \max \vert{S_{\mathbf{k}}}\vert/{b_{\mathbf{k}}}$. This is applied in multidimensional time to sums of independent random variables and martingales to yield both old and new inequalities of the Doob, Hájek-Rényi, Skorokhod and Marcinkiewicz-Zygmund types. A brief application is made to the partial sum process.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0400386-4
PII: S 0002-9939(1976)0400386-4
Keywords: Hájek-Rényi and Skorokhod inequalities, multidimensional time, martingales, partial sum process
Article copyright: © Copyright 1976 American Mathematical Society