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arXiv · 2511.22542

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

Pavel Chigansky·Marina Kleptsyna
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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 satisfies $H > 3/4$. The question posed in the title is motivated by recent findings in quantitative finance. In this note, we show that the drift in its Doob-Meyer decomposition has a derivative that is $\gamma$-H\"older continuous for any $\gamma < 2H - 3/2$.

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Pavel Chigansky, Marina Kleptsyna. 2025-11-27. How smooth is the drift of the mixed fractional Brownian motion?. https://doi.org/10.1214/26-ecp769

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