Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4 - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2009

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

Résumé

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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Dates et versions

hal-00258524 , version 1 (22-02-2008)

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Ivan Nourdin, Anthony Réveillac. Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4. 2008. ⟨hal-00258524⟩
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