How smooth is the drift of the mixed fractional Brownian motion?

Abstract: The mixed fractional Brownian motion, the sum of independent fractional and standard Brownian motions, is known to be a semimartingale if the Hurst exponent $H$ of its fractional component is greater than $3/4$. In this note, we find that the drift in its Doob-Meyer decomposition has derivative which is $γ$-Hölder for any $γ< 2H-3/2$.