TY - JOUR
T1 - Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
AU - Dzhaparidze, K.
AU - van Zanten, J.H.
N1 - MR2123205
PY - 2005
Y1 - 2005
N2 - 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. © Institute of Mathematical Statistics, 2005.
AB - 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. © Institute of Mathematical Statistics, 2005.
UR - https://www.scopus.com/pages/publications/17044403459
UR - https://www.scopus.com/inward/citedby.url?scp=17044403459&partnerID=8YFLogxK
U2 - 10.1214/009117904000000955
DO - 10.1214/009117904000000955
M3 - Article
SN - 0091-1798
VL - 33
SP - 620
EP - 644
JO - Annals of probability
JF - Annals of probability
IS - 2
ER -