Approximation of fractional brownian motion with associated hurst index separated from 1 by stochastic integrals of linear power functions

In this article we present the best uniform approximation of the fractional Brownian motion in space $ L_\infty([0, T]; L_2 (\Omega))$ by martingales of the following type $\int^t_0a(s)dW_s,$ where $W$ is a Wiener process,$a$ is a function defined by $a(s)=k_1+k_2s^\alpha, k_1,k_2\in{\mathbb R}, s\in[0, T],$ $\alpha=H-1/2,$ $H$ is the Hurst index, separated from 1, associated with the fractional Brownian motion.