Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
成果类型：
Article
署名作者：
Dzhaparidze, K; van Zanten, H
署名单位：
Vrije Universiteit Amsterdam
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117904000000955
发表日期：
2005
页码：
620-644
关键词：
摘要：
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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