On probability and moment inequalities for dependent random variables
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 \(P\{M_n> r\}\).
scientific article; zbMATH DE number 1665909