Squared chaotic random variables: new moment inequalities with applications
Probability
2015-03-10 v1 Classical Analysis and ODEs
Functional Analysis
Abstract
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 generalisation, as well as a new analytical proof, of an estimate by Frenkel (2007), and also constitute a natural real counterpart to an inequality established by Arias-de-Reyna (1998) 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), as well as to obtain a novel probabilistic representation of the remainder in Hadamard inequality of matrix analysis.
Cite
@article{arxiv.1503.02154,
title = {Squared chaotic random variables: new moment inequalities with applications},
author = {Dominique Malicet and Ivan Nourdin and Giovanni Peccati and Guillaume Poly},
journal= {arXiv preprint arXiv:1503.02154},
year = {2015}
}
Comments
22 pages