2008/03/10 by Péter Major, Peter Major, Major, Peter
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60E15 #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR) #Scientific Research and Discoveries #Stochastic processes and financial applications #math.PR #msc:60E15
paper · pdf · doi:10.48550/arxiv.0803.1453
arxiv created 2008/03/10 · openalex publication_date 2008/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.