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

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

Ivan Nourdin and Anthony Réveillac

Source: Ann. Probab. Volume 37, Number 6 (2009), 2200-2230.

Abstract

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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Primary Subjects: 60F05, 60H05, 60G15, 60H07

Keywords: Fractional Brownian motion; quartic process; change of variable formula; weighted quadratic variations; Malliavin calculus; weak convergence

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1258380787
Digital Object Identifier: doi:10.1214/09-AOP473
Zentralblatt MATH identifier: 05708799
Mathematical Reviews number (MathSciNet): MR2573556

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