A change of variable formula for the 2D fractional Brownian motion of   Hurst index bigger or equal to 1/4
  We prove a change of variable formula for the 2D fractional Brownian motion of index H bigger of equal to 1/4. For H strictly bigger than 1/4, our formula coincides with that obtained by using the rough paths theory. For H=1/4 (the more interesting case), there is an additional term that is a classical Wiener integral against an independent standard Brownian motion. 
Ivan Nourdin (PMA)