Some Processes Associated with Fractional Bessel Processes
| dc.creator | Hu, Yaozhong | |
| dc.creator | Nualart, David | |
| dc.date | 2004-02-02 | |
| dc.date.accessioned | 2026-07-07T05:05:03Z | |
| dc.date.available | 2026-07-07T05:05:03Z | |
| dc.description | Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the fractional Bessel process. Itô's formula for the fractional Brownian motion leads to the equation $ R_{t}=\sum_{i=1}^{d}\int_{0}^{t}\frac{B_{s}^{i}}{R_{s}}% dB_{s}^{i}+H(d-1)\int_{0}^{t}\frac{s^{2H-1}}{R_{s}}ds . $ In the Brownian motion case ($H=1/2$), $X_{t}=\sum_{i=1}^{d}\int_{0}^{t} frac{B_{s}^{i}}{% R_{s}}dB_{s}^{i}$ is a Brownian motion. In this paper it is shown that $X_{t}$ is \underbar{not} a fractional Brownian motion if $H\not=1/2$. We will study some other properties of this stochastic process as well. | |
| dc.identifier | https://arxiv.org/abs/math/0402019 | |
| dc.identifier | http://arxiv.org/abs/math/0402019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70035 | |
| dc.subject | Probability | |
| dc.subject | 60G15; 60G17; 60H05; 60H40 | |
| dc.title | Some Processes Associated with Fractional Bessel Processes | |
| dc.type | text |