Portal de Periódicos da CAPES

Artigo Acesso aberto Produção Nacional Revisado por pares

BIBTEX RIS

Squared chaotic random variables: New moment inequalities with applications

2015; Elsevier BV; Volume: 270; Issue: 2 Linguagem: Inglês

10.1016/j.jfa.2015.10.013

1096-0783

Dominique Malicet, Ivan Nourdin, Giovanni Peccati, Guillaume Poly,

Mathematical Analysis and Transform Methods

We prove a new family of inequalities involving squares of random variables belonging to the Wiener chaos associated with a given Gaussian field. Our result provides a substantial generalization, as well as a new analytical proof, of an estimate by Frenkel (2007) [10], and also constitutes a natural real counterpart to an inequality established by Arias-de-Reyna (1998) [2] in the framework of complex Gaussian vectors. We further show that our estimates can be used to deduce new lower bounds on homogeneous polynomials, thus partially improving results by Pinasco (2012) [19], as well as to obtain a novel probabilistic representation of the remainder in Hadamard inequality of matrix analysis.