Asymptotically normal estimation of parameters of mixed fractional Brownian motion

Abstract

We investigate the mixed fractional Brownian motion of the form Xt = σ Wt + κ BtH, driven by a standard Brownian motion W and a fractional Brownian motion BH with Hurst parameter H. We consider strongly consistent estimators of unknown model parameters (H, κ, σ) based on the equidistant observations of a trajectory. Joint asymptotic normality of these estimators is proved for H ∈ (0, 1/2) ∪ (1/2, 3/4).