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November 2009 Variations and estimators for self-similarity parameters via Malliavin calculus
Ciprian A. Tudor, Frederi G. Viens
Ann. Probab. 37(6): 2093-2134 (November 2009). DOI: 10.1214/09-AOP459

Abstract

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the self-similarity parameter H. Although, in the case of the Rosenblatt process, our estimator has non-Gaussian asymptotics for all H>1/2, we show the remarkable fact that the process’s data at time 1 can be used to construct a distinct, compensated estimator with Gaussian asymptotics for H∈(1/2, 2/3).

Citation

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Ciprian A. Tudor. Frederi G. Viens. "Variations and estimators for self-similarity parameters via Malliavin calculus." Ann. Probab. 37 (6) 2093 - 2134, November 2009. https://doi.org/10.1214/09-AOP459

Information

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

zbMATH: 1196.60036
MathSciNet: MR2573552
Digital Object Identifier: 10.1214/09-AOP459

Subjects:
Primary: 60F05, 60H05
Secondary: 60G18, 62F12

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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