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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


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).


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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.


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

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

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

Keywords: fractional Brownian motion , Hermite process , Hurst parameter , Malliavin calculus , Multiple stochastic integral , noncentral limit theorem , Quadratic Variation , Rosenblatt process , self-similarity , statistical estimation

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 6 • November 2009
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