Minimization of the entropy for a mixture of standard and fractional Brownian motions
Анотація
An entropy-type functional for the sum of a Wiener process and a fractional Brownian motion with a drift is considered in this paper. A solution of the problem of minimization of such a functional is found in the space of $L_2$ functions. Properties of the norm of the solution are investigated and a version of the problem of minimization is considered in the space of constant functions. The $L_2$ continuity of the solution of minimization problem with respect to the Hurst index is shown as a corollary of the continuity of weighted RiemannâLiouville integral operators proved in the paper.
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