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

I. Nourdin (1) , A. Réveillac

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

I. Nourdin, A. Réveillac. Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4. Annals of Probability, 2009, 37 (6), pp.2200-2230. ⟨10.1214/09-AOP473⟩. ⟨hal-00445940⟩