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

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Date
2009
Link to item file
http://hal.archives-ouvertes.fr/hal-00258524/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
Fractional Brownian motion; quartic process; change of variable formula; weighted quadratic variations; Malliavin calculus; weak convergence
Journal issue
Annals of Probability
Volume
37
Number
6
Publication date
2009
Article pages
2200-2230
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/09-AOP473
URI
https://basepub.dauphine.fr/handle/123456789/7091
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Author
Nourdin, Ivan
Réveillac, Anthony
Type
Article accepté pour publication ou publié
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.