Distance from fractional Brownian motion with associated Hurst index 0<H<1/2 to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent

Abstract

We find the best approximation of the fractional Brownian motion with the Hurst index $H\in (0,1/2)$ by Gaussian martingales of the form $\int _0^ts^{\gamma}dW_s$, where $W$ is a Wiener process, $\gamma >0$.