Statistical aspects of the fractional stochastic calculus

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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.
Published at http://dx.doi.org/10.1214/009053606000001541 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Statistics Theory, Probability, 62M09 (Primary); 60G18, 60H07, 60H10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/136473

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609295
 http://arxiv.org/abs/math/0609295
 Annals of Statistics 2007, Vol. 35, No. 3, 1183-1212
 doi:10.1214/009053606000001541

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arXiv