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Name: Krzysztof Bisewski 

Talk Title: Bounds on the expected supremum of fractional Brownian motion with drift

Abstract: Expected supremum of fractional Brownian motion with Hurst parameter $H\in(0,1]$ is one of the most fundamental quantities in theory of extremes of Gaussian processes, and yet it's value is known only in two cases (when its Hurst parameter equals 1/2 or 1). In this talk, we review the most up-to-date lower and upper bounds for this quantity for $H\in(0,1]$. Second, we introduce a new representation of fractional Brownian motion, which enables us to derive a novel lower bound. Numerical experiments suggest that our lower bound is close to the ground truth when $H

This talk is an invited talk at EVA 2021. View the programme here.