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Decoupling inequalities for polynomial chaos. (English) Zbl 0622.60026

Let \(X,X_ 1,...,X_ d\) be a sequence of independent, symmetric, identically distributed random vectors with independent components. The main subject of this paper is the so-called decoupling inequalities, i.e., inequalities of the form \[ E\phi (cQ(X,X,...,X))\leq E\phi (Q(X_ 1,X_ 2,...,X_ d))\leq E\phi (CQ(X,X,...,X)), \] where Q is a symmetric multilinear form with values in a vector space F with all ”diagonal” terms equal to zero and \(\phi\) is a convex function on F.

MSC:

60E15 Inequalities; stochastic orderings
60H99 Stochastic analysis
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