Optimal estimation of a signal perturbed by a fractional Brownian noise

Abstract

We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(θ_0,\ldots,θ_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum ${\sum }_{i=0}^n{\theta }_i{\phi }_i(t)$ over known functions ${\phi }_i(t)$, $\alli$. For the value of parameter $\thetavector$, we obtain a maximum likelihood estimate as well as Bayesian estimates for normal and uniform a priori distributions.

8 pages, 1 figure