Rosenthal's inequality for LPQD sequences
Let \((X_n)_{n\in\mathbb{N}}\) be a sequence of centered r.v.'s. Let \(S_n= X_1+ X_2+\cdots+ X_n\) and \(S_{m,n}= S_{m+n}- S_m\) with the convention that \(S_0= 0\). Suppose that the sequence \((X_n)_{n\in\mathbb{N}}\) has a finite moment of order \(r>2\). \textit{T. Birkel} [Ann. Probab. 16, No. 3, 1184-1193 (1988; Zbl 0647.60039)] showed that the Marcinkiewicz-Zygmund inequality \(A_r(n):= \sup_{m\in\mathbb{N}} E|S_{m,n}|^r\leq O(n^{r/2})\), \(n\to\infty\), holds for associated sequences. Along the line of Birkel Rosenthal's inequalities for linearly positive quadrant dependent random variables are considered. A generalization is obtained.
scientific article; zbMATH DE number 1271606