  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.
