title: Spectral correlations of fractional Brownian motion.
abstract: Fractional Brownian motion (fBm) is a ubiquitous nonstationary model for many physical processes with power-law time-averaged spectra. In this paper, we exploit the nonstationarity to derive the full spectral correlation structure of fBm. Starting from the time-varying correlation function, we derive two different time-frequency spectral correlation functions (the ambiguity function and the Kirkwood-Rihaczek spectrum), and one dual-frequency spectral correlation function. The dual-frequency spectral correlation has a surprisingly simple structure, with spectral support on three discrete lines. The theoretical predictions are verified by spectrum estimates of Monte Carlo simulations and of a time series of earthquakes with a magnitude of 7 and higher.
authors.affiliation: Department of Physics and Technology, University of Tromsø, NO-9037 Tromsø, Norway.
authors.forename: Tor Arne
authors.initials: TA
authors.lastname: Øigård
authors.forename: Alfred
authors.initials: A
authors.lastname: Hanssen
authors.forename: Louis L
authors.initials: LL
authors.lastname: Scharf