Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables
McConnell, Terry R. ; Taqqu, Murad S.
Ann. Probab., Tome 14 (1986) no. 4, p. 943-954 / Harvested from Project Euclid
Let $X^1, X^2,\ldots$ be independent copies of a sequence $X = (X_1, X_2, \ldots)$ of independent symmetric random variables. Let $M$ be a symmetric multilinear form of rank $s$ on $\mathbb{R}^\mathbb{N}$ whose components $a_{i_1,\ldots, i_s}$ relative to the standard basis of $\mathbb{R}^\mathbb{N}$ satisfy $a_{i_1,\ldots, i_s} = 0$ for all but finitely many multi-indices and whenever two indices agree. If $\phi$ is nondecreasing, convex, $\phi(0) = 0$ and $\phi$ satisfies a $\Delta_2$ growth condition then $E\phi(|M(X,\ldots, X)|) \leq cE\phi(|M(X^1,\ldots, X^s)|),$ where $c$ depends only on $\phi$ and $s$.
Publié le : 1986-07-14
Classification:  Khinchine's inequalities,  random multilinear forms,  convex functions,  60E15,  10C10
@article{1176992449,
     author = {McConnell, Terry R. and Taqqu, Murad S.},
     title = {Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 943-954},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992449}
}
McConnell, Terry R.; Taqqu, Murad S. Decoupling Inequalities for Multilinear Forms in Independent Symmetric Random Variables. Ann. Probab., Tome 14 (1986) no. 4, pp.  943-954. http://gdmltest.u-ga.fr/item/1176992449/