Parameter Estimation for Fractional Diffusion Process with Discrete Observations

Abstract

This paper deals with the problem of estimating the parameters for fractional diffusion process from discrete observations when the Hurst parameter H is unknown. With combination of several methods, such as the Donsker type approximate formula of fractional Brownian motion, quadratic variation method, and the maximum likelihood approach, we give the parameter estimations of the Hurst index, diffusion coefficients, and volatility and then prove their strong consistency. Finally, an extension for generalized fractional diffusion process and further work are briefly discussed.