Quasiasymptotics in exponential distributions by wavelet analysis
type: Item
instance of: scholarly article
title: Quasiasymptotics in exponential distributions by wavelet analysis
zbMATH Open document ID: 1271.42052
published in: Nihonkai Mathematical Journal
publication date: 2013-03-26T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.nihmj/1352124686
review text: The author considers a standard MRA within the space of square-integrable functions on the real line. The MRA expansion is then applied to exponential distributions. The aim is to analyze the properties at a point (i.e. quasiasymptotics) of such distributions with the help of the MRA expansion. The main result is that under some regularity properties one can achieve quasiasymptotics at a point (a similar result is also proved at infinity) of the continuous type if and only if the same property holds for every projection of the distribution on the elements of the MRA. It is known that the corresponding comparison function (which is continuous in this case) has also to be a regularly varying function. In the case that the distribution is quasiasymptotically bounded at zero, the results are applied to orthonormal wavelets, and some specific upper bounds for the corresponding wavelet coefficients are derived.
reviewed by: H. Šikić
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 46F12
zbMATH DE Number: 6148890
zbMATH Keywords: exponential distributions
zbMATH Keywords: multiresolution expansion
zbMATH Keywords: quasiasymptotics
zbMATH Keywords: wavelet transform
zbMATH Keywords: wavelet coefficient
author: Byung Keun Sohn
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6148890