The truncated Stieltjes moment problem solved by using kernel density functions

Gavriliadis, PN; Athanassoulis, GA

dc.contributor.author	Gavriliadis, PN	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T02:14:50Z
dc.date.available	2014-03-01T02:14:50Z
dc.date.issued	2012	en
dc.identifier.issn	03770427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30141
dc.subject	Ill-posed problem	en
dc.subject	Kernel density function	en
dc.subject	Moment asymptotics	en
dc.subject	Probability density function	en
dc.subject	Tail behavior	en
dc.subject	Truncated Stieltjes moment problem	en
dc.subject.other	Asymptotics	en
dc.subject.other	Ill posed problem	en
dc.subject.other	Kernel density function	en
dc.subject.other	Stieltjes moment problems	en
dc.subject.other	Tail behavior	en
dc.subject.other	Approximation theory	en
dc.subject.other	Probability density function	en
dc.subject.other	Theorem proving	en
dc.subject.other	Algorithms	en
dc.title	The truncated Stieltjes moment problem solved by using kernel density functions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cam.2012.05.015	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.cam.2012.05.015	en
heal.language	English	en
heal.publicationDate	2012	en
heal.abstract	In this work the problem of the approximate numerical determination of a semi-infinite supported, continuous probability density function (pdf) from a finite number of its moments is addressed. The target space is carefully defined and an approximation theorem is proved, establishing that the set of all convex superpositions of appropriate Kernel Density Functions (KDFs) is dense in this space. A solution algorithm is provided, based on the established approximate representation of the target pdf and the exploitation of some theoretical results concerning moment sequence asymptotics. The solution algorithm also permits us to recover the tail behavior of the target pdf and incorporate this information in our solution. A parsimonious formulation of the proposed solution procedure, based on a novel sequentially adaptive scheme is developed, enabling a very efficient moment data inversion. The whole methodology is fully illustrated by numerical examples. © 2012 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/j.cam.2012.05.015	en
dc.identifier.volume	236	en
dc.identifier.issue	17	en
dc.identifier.spage	4193	en
dc.identifier.epage	4213	en