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arXiv · 1707.07329

Optimal estimation of a signal perturbed by a fractional Brownian noise

A. V. Artemov·E. V. Burnaev
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Abstract

We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum $\sum_{i=0}^{n}\theta_{i}\varphi_{i}(t)$ 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.

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A. V. Artemov, E. V. Burnaev. 2017-07-23. Optimal estimation of a signal perturbed by a fractional Brownian noise. https://doi.org/10.1137/s0040585x97t987521

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