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

Abstract

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 $B$.

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)

References in corpus (6)

• Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
• Variations of the solution to a stochastic heat equation
• A change of variable formula with Itô correction term
• Central and non-central limit theorems for weighted power variations of fractional Brownian motion
• Central limit theorems for multiple Skorohod integrals
• Estimation of quadratic variation for two-parameter diffusions

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