Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
| dc.creator | Nourdin, Ivan | |
| dc.date | 2007-05-04 | |
| dc.date | 2009-01-19 | |
| dc.date.accessioned | 2026-07-07T12:30:49Z | |
| dc.date.available | 2026-07-07T12:30:49Z | |
| dc.description | The 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.description | Published 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.identifier | https://arxiv.org/abs/0705.0570 | |
| dc.identifier | http://arxiv.org/abs/0705.0570 | |
| dc.identifier | Annals of Probability 2008, Vol. 36, No. 6, 2159-2175 | |
| dc.identifier | doi:10.1214/07-AOP385 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216249 | |
| dc.subject | Probability | |
| dc.subject | 60F05, 60G15, 60H07 (Primary) | |
| dc.title | Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion | |
| dc.type | text |