McConnell, Terry R.; Taqqu, Murad S. Decoupling inequalities for multilinear forms in independent symmetric random variables. (English) Zbl 0602.60025 Ann. Probab. 14, 943-954 (1986). Let \(\tilde X=(\tilde X_ 1,\tilde X_ 2,...)\) be an independent copy of a sequence \(X=(X_ 1,X_ 2,...)\) of independent symmetric random variables. Let B be a symmetric bilinear form on \({\mathbb{R}}^{{\mathbb{N}}}\) whose matrix \(a=(a_{ij})\) with respect to the standard basis of \({\mathbb{R}}^{{\mathbb{N}}}\) satisfies \(a_{kk}=0\) for all k and \(a_{kj}=0\) for all but finitely many pairs (k,j). The aim of this paper is to establish the inequality \[ cE| B(X,X)|^ p\leq E| B(X,\tilde X)|^ p \] for \(1\leq p<\infty\). Reviewer: N.G.Gamkrelidze Cited in 17 Documents MSC: 60E15 Inequalities; stochastic orderings 11E76 Forms of degree higher than two Keywords:Khinchine’s inequalities; random multilinear forms; convex functions; symmetric bilinear form PDFBibTeX XMLCite \textit{T. R. McConnell} and \textit{M. S. Taqqu}, Ann. Probab. 14, 943--954 (1986; Zbl 0602.60025) Full Text: DOI