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arXiv: 0802.3307

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

Ivan Nourdin 1, Anthony Réveillac 2

(2008-02-22)

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.

1:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
2:	Mathématiques, Image et Applications (MIA)
	Université de La Rochelle : EA3165

Subject

:

Mathematics/Probability

Keyword(s): Fractional Brownian motion – quartic process – change of variable formula – weighted quadratic variations – Malliavin calculus – weak convergence

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From: Ivan Nourdin <>

Submitted on: Friday, 22 February 2008 13:27:43

Updated on: Wednesday, 23 April 2008 20:39:20