How smooth is the drift of the mixed fractional Brownian motion? (2511.22542v1)

Published 27 Nov 2025 in math.PR

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 $γ< 2H-3/2$.

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