Estimation in models driven by fractional Brownian motion

Berzin, Corinne; León, José R.

Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, p. 191-213 / Harvested from Project Euclid

Résumé

Let {b_H(t), t∈ℝ} be the fractional Brownian motion with parameter 00^tσ(X(u)) db_H(u)+∫₀^tμ(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.

Publié le : 2008-04-15
Classification: Central limit theorem, Estimation, Fractional Brownian motion, Gaussian processes, Hermite polynomials, 60F05, 60G15, 60G18, 60H10, 62F03, 62F12, 33C45

@article{1207948216,
     author = {Berzin, Corinne and Le\'on, Jos\'e R.},
     title = {Estimation in models driven by fractional Brownian motion},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {44},
     number = {2},
     year = {2008},
     pages = { 191-213},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1207948216}
}

Berzin, Corinne; León, José R. Estimation in models driven by fractional Brownian motion. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp.  191-213. http://gdmltest.u-ga.fr/item/1207948216/