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On the spectra of Riemann-Liouville fractional Brownian motion. (English) Zbl 0828.60099
Summary: We study the spectrum of the fractional Brownian motion of Riemann- Liouville type using two approaches, namely the double frequency spectral density and the Wigner-Ville spectrum. The bifrequency representation gives a complex-valued function which contains two distinctive terms. These terms can be identified as the diagonal and off-diagonal distribution of the spectrum in a frequency-frequency plane. The physical interpretation of these two terms is briefly discussed. A calculation of Wigner-Ville spectrum gives an alternative way of representing the spectrum of this nonstationary process in the time-frequency plane. Asymptotic approximation of the Wigner-Ville spectrum is obtained. We show that the large-time average spectrum of Riemann-Liouville fractional Brownian motion exhibits a power law in the high-frequency range.

60K40Physical applications of random processes
82C31Stochastic methods in time-dependent statistical mechanics
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