Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion

Belfadli, Rachid

doi:10.5802/ambp.281

Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
[Comportement asymptotique de la variation quadratique à poids du mouvement brownien bifractionnaire]

Belfadli, Rachid ¹

¹ Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco

Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 1, pp. 165-181.

Résumé
Abstract

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 $K \in (0, 1]$ .

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 $K \in (0, 1]$ .

MR Zbl

DOI : 10.5802/ambp.281

Classification : 60H20, 34F05, 34G20
Keywords: Bi-fractional Brownian motion, Weighted quadratic variations, Malliavan calculus.
Mot clés : Bi-fractional Brownian motion, Weighted quadratic variations, Malliavan calculus.

Affiliations des auteurs :

Belfadli, Rachid ¹

¹ Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco

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Belfadli, Rachid. Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion. Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 1, pp. 165-181. doi : 10.5802/ambp.281. http://archive.numdam.org/articles/10.5802/ambp.281/

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