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 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 γ-Hölder continuous for any γ
Fields of Study & Subjects
Stochastic processes and financial applications
Financial Risk and Volatility Modeling
Financial Markets and Investment Strategies
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026
- Language
- EN