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November 2009 Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4
Ivan Nourdin, Anthony Réveillac
Ann. Probab. 37(6): 2200-2230 (November 2009). DOI: 10.1214/09-AOP473

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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Ivan Nourdin. Anthony Réveillac. "Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H=1/4." Ann. Probab. 37 (6) 2200 - 2230, November 2009. https://doi.org/10.1214/09-AOP473

Information

Published: November 2009
First available in Project Euclid: 16 November 2009

zbMATH: 1200.60023
MathSciNet: MR2573556
Digital Object Identifier: 10.1214/09-AOP473

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

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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