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arXiv:0802.3307 [math.PR]AbstractReferencesReviewsResources

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

Ivan Nourdin, Anthony Réveillac

Published 2008-02-22, updated 2009-12-14Version 2

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 $B$.

Comments: Published in at http://dx.doi.org/10.1214/09-AOP473 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: Annals of Probability 2009, Vol. 37, No. 6, 2200-2230
Categories: math.PR
Subjects: 60F05, 60H05, 60G15, 60H07
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