Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion

dc.creatorNourdin, Ivan
dc.date2007-05-04
dc.date2009-01-19
dc.date.accessioned2026-07-07T12:30:49Z
dc.date.available2026-07-07T12:30:49Z
dc.descriptionThe present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion $B$ with Hurst index $H$. In the quadratic (resp. cubic) case, when $H<1/4$ (resp. $H<1/6$), we show by means of Malliavin calculus that the convergence holds in $L^2$ toward an explicit limit which only depends on $B$. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOP385 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0705.0570
dc.identifierhttp://arxiv.org/abs/0705.0570
dc.identifierAnnals of Probability 2008, Vol. 36, No. 6, 2159-2175
dc.identifierdoi:10.1214/07-AOP385
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216249
dc.subjectProbability
dc.subject60F05, 60G15, 60H07 (Primary)
dc.titleAsymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
dc.typetext

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