Open Access
July 2007 Statistical aspects of the fractional stochastic calculus
Ciprian A. Tudor, Frederi G. Viens
Ann. Statist. 35(3): 1183-1212 (July 2007). DOI: 10.1214/009053606000001541


We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by a fractional Brownian motion with any level of Hölder-regularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We also prove that a version of the MLE using only discrete observations is still a strongly consistent estimator.


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Ciprian A. Tudor. Frederi G. Viens. "Statistical aspects of the fractional stochastic calculus." Ann. Statist. 35 (3) 1183 - 1212, July 2007.


Published: July 2007
First available in Project Euclid: 24 July 2007

zbMATH: 1194.62097
MathSciNet: MR2341703
Digital Object Identifier: 10.1214/009053606000001541

Primary: 62M09
Secondary: 60G18 , 60H07 , 60H10

Keywords: fractional Brownian motion , Hurst parameter , Malliavin calculus , maximum likelihood estimator , Stochastic differential equation , strong consistency

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • July 2007
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