On shape-preserving probabilistic wavelet approximators Dechevsky, Lubomir en_US Penev, Spiridon en_US 2021-11-25T13:41:50Z 2021-11-25T13:41:50Z 1997 en_US
dc.description.abstract We introduce a general class of shape-preserving wavelet approximating operators (approximators) which transform cumulative distribution functions and densities into functions of the same type. Our operators can be considered as a generalization of the operators introduced by Anastassiou and Yu [1]. Further, we extend the consideration by studying the approximation properties for the whole variety of Lp:-norms, 0<p≤∞. In [1] the case p=∞ is discussed. Using the properties of integral moduli of smoothness, we obtain various approximation rates under no (or minimal) additional assumptions on the functions to be approximated. These assumptions are in terms of the function or its Riesz potential belonging to certain homogeneous Besov, Triebel-Lizorkin, Sobolev spaces, the pace BVp of functions with bounded Wiener-Young p-variation, etc en_US
dc.identifier.issn 0736-2994 en_US
dc.language English
dc.language.iso EN en_US
dc.rights CC BY-NC-ND 3.0 en_US
dc.rights.uri en_US
dc.source Legacy MARC en_US
dc.title On shape-preserving probabilistic wavelet approximators en_US
dc.type Journal Article en
dcterms.accessRights metadata only access
dspace.entity.type Publication en_US
unsw.identifier.doiPublisher en_US
unsw.relation.faculty Science
unsw.relation.ispartofissue 2 en_US
unsw.relation.ispartofjournal Stochastic Analysis and Applications en_US
unsw.relation.ispartofpagefrompageto 187-215 en_US
unsw.relation.ispartofvolume 15 en_US
unsw.relation.originalPublicationAffiliation Dechevsky, Lubomir en_US
unsw.relation.originalPublicationAffiliation Penev, Spiridon, Mathematics & Statistics, Faculty of Science, UNSW en_US School of Mathematics & Statistics *
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