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

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
37
Number
6
Publisher
Institute of Mathematical Statistics
Pages
2200-2230
Publication identifier
http://dx.doi.org/10.1214/09-AOP473
Metadata
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Author(s)
Nourdin, Ivan
Réveillac, Anthony
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

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