Open Access
July, 1987 Decoupling Inequalities for Polynomial Chaos
Stanislaw Kwapien
Ann. Probab. 15(3): 1062-1071 (July, 1987). DOI: 10.1214/aop/1176992081


Let $X, X_1,\ldots, X_d$ 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 \begin{align*}E\phi (cQ(X, X,\ldots, X)) &\leq E\phi (Q(X_1, X_2,\ldots, X_d)) \\ &\leq E\phi(CQ(X, X,\ldots, X)), \\ \end{align*} 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 $F$.


Download Citation

Stanislaw Kwapien. "Decoupling Inequalities for Polynomial Chaos." Ann. Probab. 15 (3) 1062 - 1071, July, 1987.


Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0622.60026
MathSciNet: MR893914
Digital Object Identifier: 10.1214/aop/1176992081

Primary: 60H99
Secondary: 60E15

Keywords: Decoupling inequalities , polynomial chaos

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 3 • July, 1987
Back to Top