Central and non-central limit theorems for weighted power variations of fractional Brownian motion

30 pages; minor changesInternational audienceIn this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q>=2 of the fractional Brownian motion with Hurst parameter H in (0,1), where q is an integer. The central limit holds for 1/(2q) 1-1/(2q), we show the convergence in L^2 to a stochastic integral with respect to the Hermite process of order q