## Decoupling inequalities for multilinear forms in independent symmetric random variables.(English)Zbl 0602.60025

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

### MSC:

 6e+16 Inequalities; stochastic orderings 1.1e+77 Forms of degree higher than two
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