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

Nourdin, Ivan; Réveillac, Anthony

Ann. Probab., Tome 37 (2009) no. 1, p. 2200-2230 / Harvested from Project Euclid

Résumé

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.

Publié le : 2009-11-15
Classification: Fractional Brownian motion, quartic process, change of variable formula, weighted quadratic variations, Malliavin calculus, weak convergence, 60F05, 60H05, 60G15, 60H07

@article{1258380787,
     author = {Nourdin, Ivan and R\'eveillac, Anthony},
     title = {Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 2200-2230},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258380787}
}

Nourdin, Ivan; Réveillac, Anthony. Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4. Ann. Probab., Tome 37 (2009) no. 1, pp.  2200-2230. http://gdmltest.u-ga.fr/item/1258380787/