Exact behavior of Gaussian seminorms
type: Item
instance of: scholarly article
title: Exact behavior of Gaussian seminorms
zbMATH Open document ID: 0830.60030
DOI: 10.1016/0167-7152(94)00125-R
author: Amir Dembo
author: Eddy Mayer-Wolf
author: Ofer Zeitouni
published in: Statistics \& Probability Letters
publication date: 1996-01-15T00:00:00Z
review text: Let \(\{x_i\}^\infty_{i = 1}\) be a sequence of independent standard Gaussian random variables. Consider the random variable \(z = \sum^\infty_{i = 1} x^2_i/a^2_i\), where \(\{a_i\}^\infty_{i = 1}\) is a deterministic sequence such that \(\sum^\infty_{i = 1} a^2_i < \infty\). The authors show that one may find an explicit function \(f(\varepsilon)\) such that \(\lim_{\varepsilon \to 0} f(\varepsilon) P\{z < \varepsilon\} = 1\).
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 768777
zbMATH Keywords: Gaussian norm
zbMATH Keywords: large deviations
reviewed by: Nikolai N. Leonenko
MaRDI profile type: Publication
cites work: Q4114551
cites work: On the lower tail of Gaussian seminorms
cites work: Hitting probability of a Gaussian vector with values in a Hilbert space in a sphere of small radius
cites work: Comparison results for the lower tail of Gaussian seminorms
cites work: On the lower tail probabilities of some random series
cites work: The probability of small Gaussian ellipsoids and associated conditional moments
cites work: Q4768389
description: scientific article; zbMATH DE number 768777