Maximum-likelihood estimators in the mixed fractional Brownian motion

This paper deals with the problem of estimating the parameters for the mixed fractional Brownian motion from discrete observations based on the maximum-likelihood method. The asymptotic properties, namely consistency and asymptotic normality, are presented for these estimates. By adapting the optimization algorithm, these two estimates can be efficiently computed by the computer software. The performance of the maximum-likelihood method is tested on simulated mixed fractional Brownian motion data sets, and is compared with the approach proposed by Filatova [Mixed fractional Brownian motion: Some related questions for computer network traffic modelling, International Conference on Signals and Electronic Systems, Krakow, Poland, 2008, pp. 393-396].