| Abstract: | Abstract. When the Hurst coefficient of a fractional Brownian motion  is greater than 1/2 it is possible to define a stochastic integral with respect to  , as the pathwise limit of Riemann sums, and thus to consider pathwise solutions to fractional diffusion equations. In this paper, we consider the vanishing drift case and assume that the solution X t is parameterized by θ in a compact parameter space Θ . Our main interest is the estimation of θ based on discrete time, but with very frequent observations. It is shown that the estimation problem in this context is locally asymptotically mixed normal. The asymptotic behaviour of a certain class of minimum contrast estimators is then studied and asymptotic efficiency is discussed. |
