Approximation of fractional Brownian motion by martingales
  We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given. 
Sergiy Shklyar and Georgiy Shevchenko and Yuliya Mishura and Vadym   Doroshenko and Oksana Banna
math.PR