# Lower bound for the expected supremum of fractional Brownian motion using coupling

@inproceedings{Bisewski2022LowerBF, title={Lower bound for the expected supremum of fractional Brownian motion using coupling}, author={Krzysztof Bisewski}, year={2022} }

We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index H ∈ (0, 1) over (in)finite time horizon. Extensive simulation experiments indicate that our lower bound outperforms the Monte Carlo estimates based on very dense grids for H ∈ (0, 1 2 ). Additionally, we derive the PaleyWiener-Zygmund representation of a Linear Fractional Brownian motion and give an explicit expression for the derivative of the expected supremum at H = 1 2 in…

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