Inequalities for $\max |S_k|/b_k$ where $k \in N^r$
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- by Galen R. Shorack and R. T. Smythe PDF
- Proc. Amer. Math. Soc. 54 (1976), 331-336 Request permission
Abstract:
Lemma $1$ presents a powerful general inequality for $\max |{S_{\mathbf {k}}}|/{b_{\mathbf {k}}}$. 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.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 331-336
- MSC: Primary 60G45; Secondary 60G50, 60B10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0400386-4
- MathSciNet review: 0400386