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November 2008 Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
Ivan Nourdin
Ann. Probab. 36(6): 2159-2175 (November 2008). DOI: 10.1214/07-AOP385

Abstract

The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H. In the quadratic (resp. cubic) case, when H<1/4 (resp. H<1/6), we show by means of Malliavin calculus that the convergence holds in L2 toward an explicit limit which only depends on B. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.

Citation

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Ivan Nourdin. "Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion." Ann. Probab. 36 (6) 2159 - 2175, November 2008. https://doi.org/10.1214/07-AOP385

Information

Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1155.60010
MathSciNet: MR2478679
Digital Object Identifier: 10.1214/07-AOP385

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

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 6 • November 2008
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