Statistical aspects of the fractional stochastic calculus

International audienceWe apply the techniques of stochastic integration with respect to the fractional Brownian motion and the Gaussian theory of regularity and supremum estimation to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of H\"{o}lder-regularity (any \emph{Hurst} parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We\ also prove that a basic discretized version of the MLE, is still a strongly consistent estimator