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

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

2008-02-22

arxiv.org/abs/0802.3307v2

Annals of Probability 2009, Vol. 37, No. 6, 2200-2230

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AOP473 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/09-AOP473

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 $B$.

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