We study the problem of approximation of a fractional Brownian motion with the help
of Gaussian martingales that can be presented as the integrals with respect to a Wiener process and with "similar" nonrandom integrands. We understand "similarity" in such sense that integrand is the value of fractional kernel at some point. We establish analytically and calculate numerically the upper and lower bounds for the distance between fractional Brownian motion and the space of Gaussian martingales.
