Spectral correlations of fractional Brownian motion.
نویسندگان
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.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
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ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 74 3 Pt 1 شماره
صفحات -
تاریخ انتشار 2006