Optimal estimation of a signal perturbed by a fractional Brownian noise
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 $\sum_{i=0}^{n}θ_{i}φ_{i}(t)$ over known functions $φ_i(t)$, $\alli$. For the value of parameter $\thetavector$, we obtain a maximum likelihood estimate as well as Bayesian estimates for normal and uniform a priori distributions.
math.ST↗