Some Processes Associated with Fractional Bessel Processes

dc.creatorHu, Yaozhong
dc.creatorNualart, David
dc.date2004-02-02
dc.date.accessioned2026-07-07T05:05:03Z
dc.date.available2026-07-07T05:05:03Z
dc.descriptionLet $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ 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.identifierhttps://arxiv.org/abs/math/0402019
dc.identifierhttp://arxiv.org/abs/math/0402019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70035
dc.subjectProbability
dc.subject60G15; 60G17; 60H05; 60H40
dc.titleSome Processes Associated with Fractional Bessel Processes
dc.typetext

Files

Collections