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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
Published 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)

Keywords

Probability, 60G15, 60G51, 62M15 (Primary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/74712

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503656
 http://arxiv.org/abs/math/0503656
 Annals of Probability 2005, Vol. 33, No. 2, 620-644
 doi:10.1214/009117904000000955

Collections

arXiv