Maximum Likelihood Estimation in Fractional Diffusions

In view of recent empirical findings of long memory in finance, it becomes necessary to extend the diffusion models to processes having long-range dependence. One way is to use stochastic differential equations with fractional Brownian motion (fBm) driving term, with Hurst index greater than 1/2, the solution of which is called fractional diffusion. The fBm being not a Markov process and not a semimartingale (except for the case where Hurst index is 1/2), the classical Itô calculus is not applicable to develop its theory.