Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4

Nourdin, Ivan; Réveillac, Anthony

Nourdin, Ivan; Réveillac, Anthony (2009), Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4, Annals of Probability, 37, 6, p. 2200-2230. http://dx.doi.org/10.1214/09-AOP473

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00258524/fr/

Date

2009

Journal name

Annals of Probability

Volume

Number

Publisher

Institute of Mathematical Statistics

Pages

2200-2230

Abstract (EN)

We derive the asymptotic behavior of weighted quadratic variations of fractional Brownian motion B with Hurst index H=1/4. This completes the only missing case in a very recent work by I. Nourdin, D. Nualart and C. A. Tudor. Moreover, as an application, we solve a recent conjecture of K. Burdzy and J. Swanson on the asymptotic behavior of the Riemann sums with alternating signs associated to B.

Subjects / Keywords

Fractional Brownian motion; quartic process; change of variable formula; weighted quadratic variations; Malliavin calculus; weak convergence