Spectral correlations of fractional Brownian motion.

نویسندگان

  • Tor Arne Øigård
  • Alfred Hanssen
  • Louis L Scharf
چکیده

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.

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عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 74 3 Pt 1  شماره 

صفحات  -

تاریخ انتشار 2006