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March 2005 Krein’s spectral theory and the Paley–Wiener expansion for fractional Brownian motion
Kacha Dzhaparidze, Harry van Zanten
Ann. Probab. 33(2): 620-644 (March 2005). DOI: 10.1214/009117904000000955


In this paper we develop the spectral theory of the fractional Brownian motion (fBm) using the ideas of Krein’s work on continuous analogous of orthogonal polynomials on the unit circle. We exhibit the functions which are orthogonal with respect to the spectral measure of the fBm and obtain an explicit reproducing kernel in the frequency domain. We use these results to derive an extension of the classical Paley–Wiener expansion of the ordinary Brownian motion to the fractional case.


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Kacha Dzhaparidze. Harry van Zanten. "Krein’s spectral theory and the Paley–Wiener expansion for fractional Brownian motion." Ann. Probab. 33 (2) 620 - 644, March 2005.


Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1083.60028
MathSciNet: MR2123205
Digital Object Identifier: 10.1214/009117904000000955

Primary: 60G15 , 60G51 , 62M15

Keywords: fractional Brownian motion , series expansion , spectral analysis

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 2 • March 2005
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