Stationarity and Self-similarity Characterization of the Set-indexed Fractional Brownian Motion
| dc.creator | Herbin, Erick | |
| dc.creator | Merzbach, Ely | |
| dc.date | 2007-06-23 | |
| dc.date | 2008-07-09 | |
| dc.date.accessioned | 2026-07-07T09:48:54Z | |
| dc.date.available | 2026-07-07T09:48:54Z | |
| dc.description | The set-indexed fractional Brownian motion (sifBm) has been defined by Herbin-Merzbach (2006) for indices that are subsets of a metric measure space. In this paper, the sifBm is proved to statisfy a strenghtened definition of increment stationarity. This new definition for stationarity property allows to get a complete characterization of this process by its fractal properties: The sifBm is the only set-indexed Gaussian process which is self-similar and has stationary increments. Using the fact that the sifBm is the only set-indexed process whose projection on any increasing path is a one-dimensional fractional Brownian motion, the limitation of its definition for a self-similarity parameter 0<H<1/2 is studied, as illustrated by some examples. When the indexing collection is totally ordered, the sifBm can be defined for 0<H<1. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/0706.3472 | |
| dc.identifier | http://arxiv.org/abs/0706.3472 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164389 | |
| dc.subject | Probability | |
| dc.subject | 60G10; 60G15; 60G17; 60G18 | |
| dc.title | Stationarity and Self-similarity Characterization of the Set-indexed Fractional Brownian Motion | |
| dc.type | text |