Representations of fractional Brownian motion using vibrating strings

K. Dzhaparidze, J.H. van Zanten, P. Zareba

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In this paper, we show that the moving average and series representations of fractional Brownian motion can be obtained using the spectral theory of vibrating strings. The representations are shown to be consequences of general theorems valid for a large class of second-order processes with stationary increments. Specifically, we use the 1-1 relation discovered by M.G. Krein between spectral measures of continuous second-order processes with stationary increments and differential equations describing the vibrations of a string with a certain length and mass distribution. © 2005 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)1928-1953
JournalStochastic Processes and Their Applications
Issue number12
Publication statusPublished - 2005

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