Hausdorff Dimension of the Record Set of a Fractional Brownian Motion

Abstract

We prove that the Hausdorff dimension of the record set of a fractional Brownian motion with Hurst parameter $H$ equals $H$.

References in corpus (5)

• Universal Record Statistics of Random Walks and Lévy Flights
• Record statistics for biased random walks, with an application to financial data
• Generalized arcsine laws for fractional Brownian motion
• Record statistics of a strongly correlated time series: random walks and Lévy flights
• Records in Fractal Stochastic Processes

Cited by in corpus (3)

• Mean-Field Theories for Depinning and their Experimental Signatures
• Record Ages of Scale Invariant non-Markovian Random Walks
• Full Record Statistics of 1d Random Walks