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

Ivan Nourdin; David Nualart; Ciprian Tudor

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arXiv · 0710.5639

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

Ivan Nourdin·David Nualart·Ciprian Tudor

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Abstract

In 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.

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Ivan Nourdin, David Nualart, Ciprian Tudor. 2009-08-22. Central and non-central limit theorems for weighted power variations of fractional Brownian motion. https://arxiv.org/abs/0710.5639

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