Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion

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dc.creatorDzhaparidze, Kacha
dc.creatorvan Zanten, Harry
dc.date2005-03-29
dc.date.accessioned2026-07-07T05:18:35Z
dc.date.available2026-07-07T05:18:35Z
dc.descriptionIn 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117904000000955 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503656
dc.identifierhttp://arxiv.org/abs/math/0503656
dc.identifierAnnals of Probability 2005, Vol. 33, No. 2, 620-644
dc.identifierdoi:10.1214/009117904000000955
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74712
dc.subjectProbability
dc.subject60G15, 60G51, 62M15 (Primary)
dc.titleKrein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
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