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We prove a change of variable formula for the 2D fractional Brownian motionof index H bigger of equal to 1/4. For H strictly bigger than 1/4, our formulacoincides with that obtained by using the rough paths theory. For H=1/4 (themore interesting case), there is an additional term that is a classical Wienerintegral against an independent standard Brownian motion.

A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to 1/4