Theory of Probability and Mathematical Statistics
Entropy minimization for a mixture of standard and fractional Brownian motions
V. I. Makogin, Yu. S. Mishura, H. S. Zhelezniak
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Abstract: In this paper, we consider an entropy-type functional for the sum of the Wiener process and the fractional Brownian motion with a trend. The solution of the minimization problem of such a functional in the space of $ L_2 $ -functions is found. The properties of the solution norm are investigated, and also the variant of the minimization problem on the space of constant functions is considered. As a result of the proved continuity of weighted integral Riemann-Liouville operators, $ L_2 $ -continuity of the minimization problem solution as a function of the Hurst index is shown.
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