Inverse problems for regular variation of linear filters, a cancellation property for $σ$-finite measures and identification of stable laws

Simple item page
dc.creatorJacobsen, Martin
dc.creatorMikosch, Thomas
dc.creatorRosiński, Jan
dc.creatorSamorodnitsky, Gennady
dc.date2007-12-04
dc.date2009-03-04
dc.date.accessioned2026-07-07T12:48:18Z
dc.date.available2026-07-07T12:48:18Z
dc.descriptionIn this paper, we consider certain $σ$-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have regularly varying tails as well. This turns out to be related to the presence of a particular cancellation property in $σ$-finite measures, which in turn, is related to the uniqueness of the solution of certain functional equations. The techniques we develop are applied to weighted sums of i.i.d. random variables, to products of independent random variables, and to stochastic integrals with respect to Lévy motions.
dc.descriptionPublished in at http://dx.doi.org/10.1214/08-AAP540 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0712.0576
dc.identifierhttp://arxiv.org/abs/0712.0576
dc.identifierAnnals of Applied Probability 2009, Vol. 19, No. 1, 210-242
dc.identifierdoi:10.1214/08-AAP540
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222008
dc.subjectProbability
dc.subjectStatistics Theory
dc.subject60E05 (Primary) 60E07 (Secondary)
dc.titleInverse problems for regular variation of linear filters, a cancellation property for $σ$-finite measures and identification of stable laws
dc.typetext

Files

Collections

arXiv