Estimation of Wiener--Ito integrals and polynomials of independent Gaussian random variables
| dc.creator | Major, Peter | |
| dc.date | 2008-03-10 | |
| dc.date.accessioned | 2026-07-07T09:25:58Z | |
| dc.date.available | 2026-07-07T09:25:58Z | |
| dc.description | In this paper I prove good estimates on the moments and tail distribution of $k$-fold Wiener--Itô integrals and also present their natural counterpart for polynomials of independent Gaussian random variables. The proof is based on the so-called diagram formula for Wiener--Itô integrals which yields a good representation for their products as a sum of such integrals. I intend to show in a subsequent paper that this method also yields good estimates for degenerate $U$-statistics. The main result of this paper is a generalization of the estimates of Hanson and Wright about bilinear forms of independent standard normal random variables. On the other hand, it is a weaker estimate than the main result of a paper of Latała [6]. But that paper contains an error, and it is not clear whether its result is true. This question is also discussed here. | |
| dc.identifier | https://arxiv.org/abs/0803.1453 | |
| dc.identifier | http://arxiv.org/abs/0803.1453 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156590 | |
| dc.subject | Probability | |
| dc.subject | 60E15 | |
| dc.title | Estimation of Wiener--Ito integrals and polynomials of independent Gaussian random variables | |
| dc.type | text |