Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
Annales mathématiques Blaise Pascal, Volume 17 (2010) no. 1, pp. 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: 10.5802/ambp.281
Classification: 60H20,  34F05,  34G20
Keywords: Bi-fractional Brownian motion; Weighted quadratic variations; Malliavan calculus.
Rachid Belfadli 1

1 Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco
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Rachid Belfadli. 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. https://ambp.centre-mersenne.org/articles/10.5802/ambp.281/

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