Local independence of fractional Brownian motion
| dc.creator | Norros, Ilkka | |
| dc.creator | Saksman, Eero | |
| dc.date | 2007-11-29 | |
| dc.date.accessioned | 2026-07-07T08:46:12Z | |
| dc.date.available | 2026-07-07T08:46:12Z | |
| dc.description | Let S(t,t') be the sigma-algebra generated by the differences X(s)-X(s) with s,s' in the interval(t,t'), where (X_t) is the fractional Brownian motion process with Hurst index H between 0 and 1. We prove that for any two distinct t and t' the sigma-algebras S(t-a,t+a) and S(t'-a,t'+a) are asymptotically independent as a tends to 0. We show this in the strong sense that Shannon's mutual information between these two sigma-algebras tends to zero as a tends to 0. Some generalizations and quantitative estimates are provided also. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0711.4809 | |
| dc.identifier | http://arxiv.org/abs/0711.4809 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143173 | |
| dc.subject | Probability | |
| dc.subject | Information Theory | |
| dc.subject | 60G15 (Primary); 60G18, 94A99, 60H99 (Secondary) | |
| dc.title | Local independence of fractional Brownian motion | |
| dc.type | text |