The Annals of Probability

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

Ivan Nourdin and Anthony Réveillac

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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.

Article information

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

Dates
First available in Project Euclid: 16 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1258380787

Digital Object Identifier
doi:10.1214/09-AOP473

Mathematical Reviews number (MathSciNet)
MR2573556

Zentralblatt MATH identifier
1200.60023

Subjects
Primary: 60F05: Central limit and other weak theorems 60H05: Stochastic integrals 60G15: Gaussian processes 60H07: Stochastic calculus of variations and the Malliavin calculus

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

Citation

Nourdin, Ivan; Réveillac, Anthony. Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case H =1/4. Ann. Probab. 37 (2009), no. 6, 2200--2230. doi:10.1214/09-AOP473. https://projecteuclid.org/euclid.aop/1258380787


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References

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