On probability and moment inequalities for dependent random variables (Q2752975)
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scientific article; zbMATH DE number 1665909
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On probability and moment inequalities for dependent random variables |
scientific article; zbMATH DE number 1665909 |
Statements
22 October 2001
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Banach space
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Gaussian random vector
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Hilbert space
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quantile
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uniform mixing coefficient
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Hoffmann-Jorgensen inequality
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Marcinkiewicz-Zygmund inequality
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Euler function
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On probability and moment inequalities for dependent random variables (English)
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Let \(X_k\), \(k= 1,\dots, n\), be a sequence of random variables with values in a separable Banach space with a norm. Set \(S_k= \sum^k_1 X_i\) and \(M_n= \max_{1<k<n}|S_k|\). The author modifies an inequality of \textit{J. Hoffmann-Jørgensen} [``Probability in B-spaces.'' Lecture Notes Series. No. 48. Aarhus: Aarhus Universitet, Matematisk Institut (1977; Zbl 0358.60002)] to obtain an upper estimate for the probability \(P\{M_n> r\}\).
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