Renormalized self-intersection local time for fractional Brownian motion
| dc.creator | Hu, Yaozhong | |
| dc.creator | Nualart, David | |
| dc.date | 2005-06-29 | |
| dc.date.accessioned | 2026-07-07T05:21:14Z | |
| dc.date.available | 2026-07-07T05:21:14Z | |
| dc.description | Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\in(0,1). Assume d\geq2. We prove that the renormalized self-intersection local time\ell=\int_0^T\int_0^tδ(B_t^H-B_s^H) ds dt -E\biggl(\int_0^T\int_0^tδ(B_t^H-B_s^H) ds dt\biggr) exists in L^2 if and only if H<3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a result of Yor, we show that in the case 3/4>H\geq\frac{3}{2d}, r(ε)\ell_ε converges in distribution to a normal law N(0,Tσ^2), as εtends to zero, where \ell_ε is an approximation of \ell, defined through (2), and r(ε)=|\logε|^{-1} if H=3/(2d), and r(ε)=ε^{d-3/(2H)} if 3/(2d)<H. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000017 in 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/math/0506592 | |
| dc.identifier | http://arxiv.org/abs/math/0506592 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 3, 948-983 | |
| dc.identifier | doi:10.1214/009117905000000017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75615 | |
| dc.subject | Probability | |
| dc.subject | 60G15, 60G18, 60F05, 60F25, 60H30 (Primary) | |
| dc.title | Renormalized self-intersection local time for fractional Brownian motion | |
| dc.type | text |