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Article

Optimal Estimation of a Signal Perturbed by a Fractional Brownian Noise

Theory of Probability and Its Applications. 2016. Vol. 60. No. 1. P. 126-134.
Artemov A., Burnaev E.

We consider the problem of optimal estimation of the value of a vector parameter \thetavector=(\theta_0,...,\theta_n)^⊤ of the drift term in a fractional Brownian motion represented by the finite sum i=0^nii(t) over known functions \varphi_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.