A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$
| dc.creator | Unterberger, Jeremie | |
| dc.date | 2008-08-26 | |
| dc.date | 2008-08-29 | |
| dc.date.accessioned | 2026-07-07T09:59:00Z | |
| dc.date.available | 2026-07-07T09:59:00Z | |
| dc.description | Let $B=(B^{(1)},B^{(2)})$ be a two-dimensional fractional Brownian motion with Hurst index $α\in (0,1/4)$. Using an analytic approximation $B(η)$ of $B$ introduced in \cite{Unt08}, we prove that the rescaled Lévy area process $(s,t)\to η^{\half(1-4α)}\int_s^t dB_{t_1}^{(1)}(η) \int_s^{t_1} dB_{t_2}^{(2)}(η)$ converges in law to $W_t-W_s$ where $W$ is a Brownian motion independent from $B$. The method relies on a very general scheme of analysis of singularities of analytic functions, applied to the moments of finite-dimensional distributions of the Lévy area. | |
| dc.description | 70 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0808.3458 | |
| dc.identifier | http://arxiv.org/abs/0808.3458 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167883 | |
| dc.subject | Probability | |
| dc.subject | 60F05, 60G15, 60G18, 60H05 | |
| dc.title | A central limit theorem for the rescaled Lévy area of two-dimensional fractional Brownian motion with Hurst index $H<1/4$ | |
| dc.type | text |