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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00258524/fr/Date
2009Journal name
Annals of ProbabilityVolume
37Number
6Publisher
Institute of Mathematical Statistics
Pages
2200-2230
Publication identifier
Metadata
Show full item recordAbstract (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 convergenceRelated items
Showing items related by title and author.
-
Réveillac, Anthony (2009) Article accepté pour publication ou publié
-
The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6 Nourdin, Ivan; Réveillac, Anthony; Swanson, Jason (2010) Article accepté pour publication ou publié
-
Réveillac, Anthony; Pakkanen, Mikko S. (2016) Article accepté pour publication ou publié
-
Réveillac, Anthony; Stauch, Michael; Tudor, Ciprian A. (2012) Article accepté pour publication ou publié
-
Réveillac, Anthony (2009) Article accepté pour publication ou publié