Discretizing the fractional Levy area
| dc.creator | Neuenkirch, Andreas | |
| dc.creator | Tindel, Samy | |
| dc.creator | Unterberger, Jérémie | |
| dc.date | 2009-02-03 | |
| dc.date.accessioned | 2026-07-07T12:37:18Z | |
| dc.date.available | 2026-07-07T12:37:18Z | |
| dc.description | In this article, we give sharp bounds for the Euler- and trapezoidal discretization of the Levy area associated to a d-dimensional fractional Brownian motion. We show that there are three different regimes for the exact root mean-square convergence rate of the Euler scheme. For H<3/4 the exact convergence rate is n^{-2H+1/2}, where n denotes the number of the discretization subintervals, while for H=3/4 it is n^{-1} (log(n))^{1/2} and for H>3/4 the exact rate is n^{-1}. Moreover, the trapezoidal scheme has exact convergence rate n^{-2H+1/2} for H>1/2. Finally, we also derive the asymptotic error distribution of the Euler scheme. For H lesser than 3/4 one obtains a Gaussian limit, while for H>3/4 the limit distribution is of Rosenblatt type. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/0902.0497 | |
| dc.identifier | http://arxiv.org/abs/0902.0497 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218391 | |
| dc.subject | Probability | |
| dc.subject | 60H35 (Primary) 60H07, 60H10, 65C30 (Secondary) | |
| dc.title | Discretizing the fractional Levy area | |
| dc.type | text |