# Estimation in models driven by fractional brownian motion

• Volume: 44, Issue: 2, page 191-213
• ISSN: 0246-0203

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## Abstract

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Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0&lt;H&lt;1. When 1/2&lt;H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ  x and μ(x)=μ or μ(x)=μ  x, 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(⋅) in the above more general models based in the asymptotic behavior of functionals of the 2nd-order increments of the fBm.

## How to cite

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Berzin, Corinne, and León, José R.. "Estimation in models driven by fractional brownian motion." Annales de l'I.H.P. Probabilités et statistiques 44.2 (2008): 191-213. <http://eudml.org/doc/77966>.

@article{Berzin2008,
abstract = {Let \{bH(t), t∈ℝ\} be the fractional brownian motion with parameter 0&lt;H&lt;1. When 1/2&lt;H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ  x and μ(x)=μ or μ(x)=μ  x, 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(⋅) in the above more general models based in the asymptotic behavior of functionals of the 2nd-order increments of the fBm.},
author = {Berzin, Corinne, León, José R.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {central limit theorem; estimation; fractional brownian motion; gaussian processes; Hermite polynomials; Gaussian processes},
language = {eng},
number = {2},
pages = {191-213},
publisher = {Gauthier-Villars},
title = {Estimation in models driven by fractional brownian motion},
url = {http://eudml.org/doc/77966},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Berzin, Corinne
AU - León, José R.
TI - Estimation in models driven by fractional brownian motion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 2
SP - 191
EP - 213
AB - Let {bH(t), t∈ℝ} be the fractional brownian motion with parameter 0&lt;H&lt;1. When 1/2&lt;H, we consider diffusion equations of the type X(t)=c+∫0tσ(X(u)) dbH(u)+∫0tμ(X(u)) du. In different particular models where σ(x)=σ or σ(x)=σ  x and μ(x)=μ or μ(x)=μ  x, 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(⋅) in the above more general models based in the asymptotic behavior of functionals of the 2nd-order increments of the fBm.
LA - eng
KW - central limit theorem; estimation; fractional brownian motion; gaussian processes; Hermite polynomials; Gaussian processes
UR - http://eudml.org/doc/77966
ER -

## References

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8. [8] S. J. Lin. Stochastic analysis of fractional Brownian motions. Stochastics Stochastics Rep. 55 (1995) 121–140. Zbl0886.60076MR1382288
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