Estimation in models driven by fractional Brownian motion

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dc.creatorBerzin, Corinne
dc.creatorLeón, José R.
dc.date2008-05-22
dc.date.accessioned2026-07-07T12:19:10Z
dc.date.available2026-07-07T12:19:10Z
dc.descriptionLet $\{b_H(t),t\in\mathbb{R}\}$ be the fractional Brownian motion with parameter $0<H<1$. When $1/2<H$, we consider diffusion equations of the type \[X(t)=c+\int_0^tσ\bigl(X(u)\bigr)\mathrm {d}b_H(u)+\int _0^tμ\bigl(X(u)\bigr)\mathrm {d}u.\] In different particular models where $σ(x)=σ$ or $σ(x)=σx$ and $μ(x)=μ$ or $μ(x)=μx$, we propose a central limit theorem for estimators of $H$ and of $σ$ based on regression methods. Then we give tests of the hypothesis on $σ$ for these models. We also consider functional estimation on $σ(\cdot)$ in the above more general models based in the asymptotic behavior of functionals of the 2nd-order increments of the fBm.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AIHP105 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0805.3394
dc.identifierhttp://arxiv.org/abs/0805.3394
dc.identifierAnnales de l'Institut Henri Poincaré - Probabilités et Statistiques 2008, Vol. 44, No. 2, 191-213
dc.identifierdoi:10.1214/07-AIHP105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212659
dc.subjectProbability
dc.subject60F05, 60G15, 60G18, 60H10, 62F03, 62F12, 33C45 (Primary)
dc.titleEstimation in models driven by fractional Brownian motion
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