Statistical aspects of the fractional stochastic calculus

Details Statistical aspects of the fractional stochastic calculus Statistical aspects of the fractional stochastic calculus

2006-09-11

arxiv.org/abs/math/0609295v2

Annals of Statistics 2007, Vol. 35, No. 3, 1183-1212

Mathematics

Statistics Theory

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

Scientific paper

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 H\"{o}lder-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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