Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 1, p. 165-181

We prove, by means of Malliavin calculus, the convergence in L 2 of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters H and K, when H<1/4 and K(0,1].

Nous utilisons le calcul de Malliavin pour montrer la convergence dans L 2 de la variation quadratique à poids du mouvement brownien bifractionnaire (biFBM) d’indices H et K lorsque H<1/4 et K(0,1].

DOI : https://doi.org/10.5802/ambp.281
Classification:  60H20,  34F05,  34G20
Keywords: Bi-fractional Brownian motion; Weighted quadratic variations; Malliavan calculus.
@article{AMBP_2010__17_1_165_0,
     author = {Belfadli, Rachid},
     title = {Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion},
     journal = {Annales math\'ematiques Blaise Pascal},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {17},
     number = {1},
     year = {2010},
     pages = {165-181},
     doi = {10.5802/ambp.281},
     mrnumber = {2674657},
     zbl = {1196.60066},
     language = {en},
     url = {http://www.numdam.org/item/AMBP_2010__17_1_165_0}
}
Belfadli, Rachid. Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion. Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 1, pp. 165-181. doi : 10.5802/ambp.281. http://www.numdam.org/item/AMBP_2010__17_1_165_0/

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